exp_final_test – Complete Experiment Report

Base

▼

Base_Gaussian (MvNormal, mu, 12 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0, 0) -2.078 0.0498 -0.905
SMC (0, 0) -1.772 0.0903 -0.719
Metro (0, 0) 1.885 0.0818 1.829
DEMetro_Z (0, 0) 5.101 6.41e-05 2.695
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -8.309 4.55e-06 -2.399
Metro_vs_SMC 0 2.475 0.0309 0.714
Metro_vs_DEMetro_Z 0 -0.865 0.406 -0.250
HMC_vs_Metro 0 -2.719 0.02 -0.785
HMC_vs_SMC 0 -0.530 0.607 -0.153
DEMetro_Z_vs_SMC 0 6.548 4.15e-05 1.890
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0, 0) 0.018 0.025 0.008 -0.905
SMC (0, 0) 0.019 0.025 0.008 -0.719
Metro (0, 0) 0.040 0.025 0.008 1.829
DEMetro_Z (0, 0) 0.047 0.025 0.008 2.695
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0, 0) 1.121 0.274 0.430
SMC (0, 0) -0.037 0.971 -0.018
Metro (0, 0) 1.245 0.227 0.595
DEMetro_Z (0, 0) 0.578 0.57 0.277
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.929 0.373 0.268
Metro_vs_DEMetro_Z 0 0.641 0.535 0.185
HMC_vs_Metro 0 -0.571 0.579 -0.165
HMC_vs_DEMetro_Z 0 0.326 0.751 0.094
Metro_vs_SMC 0 1.553 0.149 0.448
DEMetro_Z_vs_SMC 0 0.614 0.552 0.177
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0, 0) 0.036 0.030 0.013 0.430
SMC (0, 0) 0.030 0.030 0.013 -0.018
Metro (0, 0) 0.038 0.030 0.013 0.595
DEMetro_Z (0, 0) 0.034 0.030 0.013 0.277
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0, 0) -1.658 0.114 -0.865
SMC (0, 0) -2.133 0.045 -1.006
Metro (0, 0) 2.367 0.0358 3.448
DEMetro_Z (0, 0) 6.598 1.32e-05 5.703
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -1.467 0.171 -0.423
DEMetro_Z_vs_SMC 0 7.708 9.28e-06 2.225
HMC_vs_DEMetro_Z 0 -7.200 1.75e-05 -2.079
HMC_vs_Metro 0 -2.879 0.015 -0.831
HMC_vs_SMC 0 0.351 0.733 0.101
Metro_vs_SMC 0 2.899 0.0145 0.837
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0, 0) 0.029 0.032 0.004 -0.865
SMC (0, 0) 0.028 0.032 0.004 -1.006
Metro (0, 0) 0.046 0.032 0.004 3.448
DEMetro_Z (0, 0) 0.056 0.032 0.004 5.703
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0, 0) -2.071 0.0504 -0.808
SMC (0, 0) -1.961 0.0629 -0.755
Metro (0, 0) 1.673 0.119 1.919
DEMetro_Z (0, 0) 4.303 0.000631 3.131
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 5.293 0.000255 1.528
HMC_vs_Metro 0 -2.407 0.0348 -0.695
Metro_vs_DEMetro_Z 0 -0.985 0.346 -0.284
HMC_vs_SMC 0 -0.190 0.853 -0.055
Metro_vs_SMC 0 2.304 0.0417 0.665
HMC_vs_DEMetro_Z 0 -5.401 0.000216 -1.559
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0, 0) 0.013 0.016 0.004 -0.808
SMC (0, 0) 0.013 0.016 0.004 -0.755
Metro (0, 0) 0.023 0.016 0.004 1.919
DEMetro_Z (0, 0) 0.027 0.016 0.004 3.131
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0, 0) -2.509 0.0201 -0.964
SMC (0, 0) -2.399 0.0254 -1.015
Metro (0, 0) 0.841 0.412 0.502
DEMetro_Z (0, 0) 2.239 0.039 1.367
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -3.563 0.00445 -1.029
Metro_vs_SMC 0 2.438 0.0329 0.704
Metro_vs_DEMetro_Z 0 -0.996 0.341 -0.288
HMC_vs_Metro 0 -2.923 0.0139 -0.844
HMC_vs_SMC 0 0.159 0.877 0.046
DEMetro_Z_vs_SMC 0 4.088 0.0018 1.180
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0, 0) 0.017 0.025 0.008 -0.964
SMC (0, 0) 0.017 0.025 0.008 -1.015
Metro (0, 0) 0.029 0.025 0.008 0.502
DEMetro_Z (0, 0) 0.036 0.025 0.008 1.367
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0, 0) 2.035 0.0565 1.110
SMC (0, 0) -0.800 0.433 -0.367
Metro (0, 0) 1.684 0.11 0.960
DEMetro_Z (0, 0) 2.108 0.0488 1.140
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 3.331 0.0067 0.961
Metro_vs_DEMetro_Z 0 -0.305 0.766 -0.088
HMC_vs_Metro 0 0.181 0.86 0.052
HMC_vs_DEMetro_Z 0 -0.052 0.959 -0.015
Metro_vs_SMC 0 1.894 0.0849 0.547
DEMetro_Z_vs_SMC 0 2.384 0.0363 0.688
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0, 0) 0.045 0.030 0.013 1.110
SMC (0, 0) 0.025 0.030 0.013 -0.367
Metro (0, 0) 0.043 0.030 0.013 0.960
DEMetro_Z (0, 0) 0.045 0.030 0.013 1.140
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0, 0) -0.633 0.534 -0.316
SMC (0, 0) -2.821 0.0102 -1.271
Metro (0, 0) 2.280 0.038 1.727
DEMetro_Z (0, 0) 5.099 0.000175 4.460
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -2.523 0.0283 -0.728
DEMetro_Z_vs_SMC 0 6.709 3.34e-05 1.937
HMC_vs_DEMetro_Z 0 -4.888 0.000481 -1.411
HMC_vs_Metro 0 -2.576 0.0258 -0.744
HMC_vs_SMC 0 2.214 0.0489 0.639
Metro_vs_SMC 0 3.533 0.00469 1.020
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0, 0) 0.031 0.032 0.004 -0.316
SMC (0, 0) 0.027 0.032 0.004 -1.271
Metro (0, 0) 0.039 0.032 0.004 1.727
DEMetro_Z (0, 0) 0.051 0.032 0.004 4.460
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0, 0) -0.783 0.442 -0.333
SMC (0, 0) -2.261 0.0341 -0.980
Metro (0, 0) 1.028 0.317 0.568
DEMetro_Z (0, 0) 3.799 0.00156 2.472
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 5.778 0.000123 1.668
HMC_vs_Metro 0 -1.463 0.171 -0.422
Metro_vs_DEMetro_Z 0 -2.909 0.0142 -0.840
HMC_vs_SMC 0 1.596 0.139 0.461
Metro_vs_SMC 0 2.432 0.0333 0.702
HMC_vs_DEMetro_Z 0 -4.215 0.00145 -1.217
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0, 0) 0.015 0.016 0.004 -0.333
SMC (0, 0) 0.013 0.016 0.004 -0.980
Metro (0, 0) 0.018 0.016 0.004 0.568
DEMetro_Z (0, 0) 0.025 0.016 0.004 2.472
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
(0, 0) HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
(0, 0) HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
(0, 0)
Chain
(0, 0)

Base_Gaussian_Seed (MvNormal, mu, 12 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0, 0) -0.544 0.593 -0.183
SMC (0, 0) -0.182 0.857 -0.068
Metro (0, 0) 3.252 0.00424 1.734
DEMetro_Z (0, 0) 2.609 0.0191 1.728
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -3.644 0.00386 -1.052
Metro_vs_SMC 0 3.518 0.00481 1.016
Metro_vs_DEMetro_Z 0 0.009 0.993 0.003
HMC_vs_Metro 0 -4.839 0.00052 -1.397
HMC_vs_SMC 0 -0.317 0.757 -0.092
DEMetro_Z_vs_SMC 0 2.351 0.0384 0.679
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0, 0) 0.016 0.018 0.011 -0.183
SMC (0, 0) 0.018 0.018 0.011 -0.068
Metro (0, 0) 0.037 0.018 0.011 1.734
DEMetro_Z (0, 0) 0.037 0.018 0.011 1.728
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0, 0) -0.133 0.896 -0.064
SMC (0, 0) -1.255 0.223 -0.481
Metro (0, 0) 0.296 0.771 0.189
DEMetro_Z (0, 0) 2.084 0.0549 1.542
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 1.171 0.266 0.338
Metro_vs_DEMetro_Z 0 -1.796 0.1 -0.518
HMC_vs_Metro 0 -0.449 0.662 -0.130
HMC_vs_DEMetro_Z 0 -3.240 0.00787 -0.935
Metro_vs_SMC 0 1.458 0.173 0.421
DEMetro_Z_vs_SMC 0 3.079 0.0105 0.889
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0, 0) 0.031 0.032 0.011 -0.064
SMC (0, 0) 0.027 0.032 0.011 -0.481
Metro (0, 0) 0.034 0.032 0.011 0.189
DEMetro_Z (0, 0) 0.049 0.032 0.011 1.542
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0, 0) -1.080 0.295 -0.352
SMC (0, 0) -0.777 0.446 -0.322
Metro (0, 0) 3.770 0.00163 2.410
DEMetro_Z (0, 0) 4.511 0.000459 3.536
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -1.216 0.25 -0.351
DEMetro_Z_vs_SMC 0 4.321 0.00121 1.247
HMC_vs_DEMetro_Z 0 -5.577 0.000166 -1.610
HMC_vs_Metro 0 -5.662 0.000146 -1.635
HMC_vs_SMC 0 -0.081 0.937 -0.023
Metro_vs_SMC 0 4.712 0.000637 1.360
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0, 0) 0.027 0.029 0.007 -0.352
SMC (0, 0) 0.027 0.029 0.007 -0.322
Metro (0, 0) 0.045 0.029 0.007 2.410
DEMetro_Z (0, 0) 0.052 0.029 0.007 3.536
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0, 0) -0.474 0.641 -0.163
SMC (0, 0) -1.037 0.311 -0.441
Metro (0, 0) 3.159 0.00631 2.189
DEMetro_Z (0, 0) 4.427 0.000422 2.903
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 4.507 0.000891 1.301
HMC_vs_Metro 0 -4.149 0.00162 -1.198
Metro_vs_DEMetro_Z 0 -0.874 0.401 -0.252
HMC_vs_SMC 0 0.690 0.505 0.199
Metro_vs_SMC 0 4.580 0.00079 1.322
HMC_vs_DEMetro_Z 0 -5.572 0.000167 -1.608
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0, 0) 0.013 0.014 0.004 -0.163
SMC (0, 0) 0.012 0.014 0.004 -0.441
Metro (0, 0) 0.022 0.014 0.004 2.189
DEMetro_Z (0, 0) 0.025 0.014 0.004 2.903
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0, 0) 0.270 0.789 0.107
SMC (0, 0) -0.398 0.695 -0.159
Metro (0, 0) 1.278 0.215 0.545
DEMetro_Z (0, 0) 2.412 0.026 1.248
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -2.569 0.0261 -0.742
Metro_vs_SMC 0 1.396 0.19 0.403
Metro_vs_DEMetro_Z 0 -1.196 0.257 -0.345
HMC_vs_Metro 0 -0.876 0.4 -0.253
HMC_vs_SMC 0 0.720 0.487 0.208
DEMetro_Z_vs_SMC 0 3.540 0.00463 1.022
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0, 0) 0.020 0.018 0.011 0.107
SMC (0, 0) 0.017 0.018 0.011 -0.159
Metro (0, 0) 0.024 0.018 0.011 0.545
DEMetro_Z (0, 0) 0.032 0.018 0.011 1.248
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0, 0) 0.190 0.851 0.104
SMC (0, 0) -3.001 0.00661 -1.283
Metro (0, 0) 0.544 0.594 0.384
DEMetro_Z (0, 0) 4.001 0.00117 2.937
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 2.298 0.0422 0.663
Metro_vs_DEMetro_Z 0 -2.744 0.0191 -0.792
HMC_vs_Metro 0 -0.309 0.763 -0.089
HMC_vs_DEMetro_Z 0 -3.096 0.0102 -0.894
Metro_vs_SMC 0 2.151 0.0546 0.621
DEMetro_Z_vs_SMC 0 5.164 0.000311 1.491
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0, 0) 0.033 0.032 0.011 0.104
SMC (0, 0) 0.018 0.032 0.011 -1.283
Metro (0, 0) 0.036 0.032 0.011 0.384
DEMetro_Z (0, 0) 0.064 0.032 0.011 2.937
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0, 0) 0.837 0.412 0.319
SMC (0, 0) -1.836 0.0817 -0.641
Metro (0, 0) 2.456 0.0225 1.068
DEMetro_Z (0, 0) 6.305 3.78e-06 3.123
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -3.332 0.00669 -0.962
DEMetro_Z_vs_SMC 0 10.048 7.05e-07 2.900
HMC_vs_DEMetro_Z 0 -6.797 2.96e-05 -1.962
HMC_vs_Metro 0 -1.545 0.151 -0.446
HMC_vs_SMC 0 3.273 0.00742 0.945
Metro_vs_SMC 0 4.066 0.00187 1.174
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0, 0) 0.031 0.029 0.007 0.319
SMC (0, 0) 0.025 0.029 0.007 -0.641
Metro (0, 0) 0.036 0.029 0.007 1.068
DEMetro_Z (0, 0) 0.050 0.029 0.007 3.123
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC (0, 0) 1.199 0.243 0.501
SMC (0, 0) -1.386 0.18 -0.588
Metro (0, 0) 1.717 0.101 0.832
DEMetro_Z (0, 0) 5.391 2.82e-05 2.664
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 7.372 1.41e-05 2.128
HMC_vs_Metro 0 -0.571 0.58 -0.165
Metro_vs_DEMetro_Z 0 -3.024 0.0116 -0.873
HMC_vs_SMC 0 2.673 0.0217 0.772
Metro_vs_SMC 0 2.682 0.0213 0.774
HMC_vs_DEMetro_Z 0 -4.089 0.00179 -1.180
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC (0, 0) 0.016 0.014 0.004 0.501
SMC (0, 0) 0.011 0.014 0.004 -0.588
Metro (0, 0) 0.017 0.014 0.004 0.832
DEMetro_Z (0, 0) 0.024 0.014 0.004 2.664
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
(0, 0) HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
(0, 0) HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
(0, 0)
Chain
(0, 0)

Only_attr

▼

Vary_only_Correlation (MvNormal, correlation, 12 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -2.644 0.0151 -0.984
HMC 0.3 -0.503 0.621 -0.250
HMC 0.5 1.219 0.237 0.608
HMC 0.9 0.570 0.575 0.250
HMC 0.95 0.750 0.462 0.376
HMC 0.99 1.363 0.191 0.854
SMC 0.0 -2.871 0.00903 -1.288
SMC 0.3 -0.415 0.683 -0.214
SMC 0.5 -0.929 0.363 -0.412
SMC 0.9 0.502 0.621 0.226
SMC 0.95 -0.426 0.675 -0.146
SMC 0.99 0.625 0.539 0.217
Metro 0.0 2.021 0.0567 0.976
Metro 0.3 2.856 0.00964 1.376
Metro 0.5 0.444 0.663 0.272
Metro 0.9 2.666 0.0205 3.582
Metro 0.95 6.056 6.66e-05 10.993
Metro 0.99 4.344 0.00113 14.022
DEMetro_Z 0.0 1.801 0.0952 1.853
DEMetro_Z 0.3 3.707 0.00276 4.057
DEMetro_Z 0.5 2.894 0.00987 1.685
DEMetro_Z 0.9 2.232 0.0421 1.762
DEMetro_Z 0.95 2.514 0.0232 1.696
DEMetro_Z 0.99 5.132 4.49e-05 2.394
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -2.733 0.0195 -0.789
HMC_vs_DEMetro_Z 0.3 -3.706 0.00347 -1.070
HMC_vs_DEMetro_Z 0.5 -1.399 0.189 -0.404
HMC_vs_DEMetro_Z 0.9 -1.730 0.111 -0.500
HMC_vs_DEMetro_Z 0.95 -1.559 0.147 -0.450
HMC_vs_DEMetro_Z 0.99 -2.128 0.0568 -0.614
Metro_vs_SMC 0.0 5.828 0.000114 1.682
Metro_vs_SMC 0.3 2.709 0.0203 0.782
Metro_vs_SMC 0.5 0.956 0.36 0.276
Metro_vs_SMC 0.9 2.337 0.0394 0.675
Metro_vs_SMC 0.95 6.443 4.79e-05 1.860
Metro_vs_SMC 0.99 4.342 0.00117 1.253
Metro_vs_DEMetro_Z 0.0 -0.879 0.398 -0.254
Metro_vs_DEMetro_Z 0.3 -2.367 0.0374 -0.683
Metro_vs_DEMetro_Z 0.5 -1.497 0.162 -0.432
Metro_vs_DEMetro_Z 0.9 1.279 0.227 0.369
Metro_vs_DEMetro_Z 0.95 4.975 0.000418 1.436
Metro_vs_DEMetro_Z 0.99 3.634 0.00393 1.049
HMC_vs_Metro 0.0 -4.537 0.000847 -1.310
HMC_vs_Metro 0.3 -2.726 0.0197 -0.787
HMC_vs_Metro 0.5 0.664 0.521 0.192
HMC_vs_Metro 0.9 -2.244 0.0464 -0.648
HMC_vs_Metro 0.95 -6.168 7.03e-05 -1.780
HMC_vs_Metro 0.99 -4.254 0.00136 -1.228
HMC_vs_SMC 0.0 0.820 0.43 0.237
HMC_vs_SMC 0.3 -0.092 0.928 -0.027
HMC_vs_SMC 0.5 2.194 0.0506 0.633
HMC_vs_SMC 0.9 0.056 0.957 0.016
HMC_vs_SMC 0.95 1.190 0.259 0.344
HMC_vs_SMC 0.99 1.060 0.312 0.306
DEMetro_Z_vs_SMC 0.0 3.453 0.0054 0.997
DEMetro_Z_vs_SMC 0.3 3.692 0.00355 1.066
DEMetro_Z_vs_SMC 0.5 3.729 0.00333 1.076
DEMetro_Z_vs_SMC 0.9 1.889 0.0856 0.545
DEMetro_Z_vs_SMC 0.95 3.372 0.00623 0.974
DEMetro_Z_vs_SMC 0.99 6.481 4.55e-05 1.871
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.017 0.025 0.008 -0.984
HMC 0.3 0.018 0.020 0.009 -0.250
HMC 0.5 0.030 0.024 0.010 0.608
HMC 0.9 0.023 0.019 0.014 0.250
HMC 0.95 0.021 0.017 0.012 0.376
HMC 0.99 0.032 0.018 0.016 0.854
SMC 0.0 0.015 0.025 0.008 -1.288
SMC 0.3 0.018 0.020 0.009 -0.214
SMC 0.5 0.020 0.024 0.010 -0.412
SMC 0.9 0.023 0.019 0.014 0.226
SMC 0.95 0.015 0.017 0.012 -0.146
SMC 0.99 0.022 0.018 0.016 0.217
Metro 0.0 0.033 0.025 0.008 0.976
Metro 0.3 0.033 0.020 0.009 1.376
Metro 0.5 0.026 0.024 0.010 0.272
Metro 0.9 0.069 0.019 0.014 3.582
Metro 0.95 0.145 0.017 0.012 10.993
Metro 0.99 0.238 0.018 0.016 14.022
DEMetro_Z 0.0 0.040 0.025 0.008 1.853
DEMetro_Z 0.3 0.058 0.020 0.009 4.057
DEMetro_Z 0.5 0.040 0.024 0.010 1.685
DEMetro_Z 0.9 0.044 0.019 0.014 1.762
DEMetro_Z 0.95 0.037 0.017 0.012 1.696
DEMetro_Z 0.99 0.056 0.018 0.016 2.394
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 1.043 0.308 0.462
HMC 0.3 0.278 0.784 0.151
HMC 0.5 1.587 0.127 0.716
HMC 0.9 1.565 0.14 1.296
HMC 0.95 4.760 9.52e-05 2.010
HMC 0.99 -2.090 0.0486 -0.798
SMC 0.0 -0.307 0.762 -0.121
SMC 0.3 -0.797 0.434 -0.339
SMC 0.5 -0.606 0.552 -0.214
SMC 0.9 0.425 0.675 0.191
SMC 0.95 0.812 0.426 0.394
SMC 0.99 -2.120 0.0466 -0.758
Metro 0.0 1.958 0.0692 1.442
Metro 0.3 3.448 0.00284 1.917
Metro 0.5 3.377 0.003 1.668
Metro 0.9 2.887 0.00985 1.630
Metro 0.95 5.064 0.000253 6.019
Metro 0.99 2.917 0.0138 11.062
DEMetro_Z 0.0 3.326 0.00378 1.877
DEMetro_Z 0.3 2.143 0.0478 1.407
DEMetro_Z 0.5 2.653 0.0178 1.844
DEMetro_Z 0.9 1.852 0.0846 1.445
DEMetro_Z 0.95 0.972 0.346 0.660
DEMetro_Z 0.99 0.720 0.482 0.491
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 1.296 0.222 0.374
HMC_vs_SMC 0.3 1.190 0.259 0.344
HMC_vs_SMC 0.5 2.494 0.0298 0.720
HMC_vs_SMC 0.9 1.278 0.228 0.369
HMC_vs_SMC 0.95 2.937 0.0135 0.848
HMC_vs_SMC 0.99 -0.105 0.918 -0.030
Metro_vs_DEMetro_Z 0.0 -0.702 0.497 -0.203
Metro_vs_DEMetro_Z 0.3 0.833 0.423 0.240
Metro_vs_DEMetro_Z 0.5 -0.319 0.756 -0.092
Metro_vs_DEMetro_Z 0.9 0.233 0.82 0.067
Metro_vs_DEMetro_Z 0.95 4.911 0.000463 1.418
Metro_vs_DEMetro_Z 0.99 2.558 0.0266 0.738
HMC_vs_Metro 0.0 -1.351 0.204 -0.390
HMC_vs_Metro 0.3 -3.625 0.00399 -1.046
HMC_vs_Metro 0.5 -1.550 0.149 -0.447
HMC_vs_Metro 0.9 -0.311 0.762 -0.090
HMC_vs_Metro 0.95 -3.340 0.0066 -0.964
HMC_vs_Metro 0.99 -3.114 0.00986 -0.899
HMC_vs_DEMetro_Z 0.0 -2.757 0.0187 -0.796
HMC_vs_DEMetro_Z 0.3 -1.867 0.0888 -0.539
HMC_vs_DEMetro_Z 0.5 -1.629 0.132 -0.470
HMC_vs_DEMetro_Z 0.9 -0.128 0.901 -0.037
HMC_vs_DEMetro_Z 0.95 2.040 0.0661 0.589
HMC_vs_DEMetro_Z 0.99 -1.879 0.087 -0.542
Metro_vs_SMC 0.0 2.140 0.0556 0.618
Metro_vs_SMC 0.3 4.428 0.00101 1.278
Metro_vs_SMC 0.5 4.813 0.000542 1.389
Metro_vs_SMC 0.9 1.966 0.075 0.568
Metro_vs_SMC 0.95 4.444 0.000988 1.283
Metro_vs_SMC 0.99 3.156 0.00914 0.911
DEMetro_Z_vs_SMC 0.0 3.049 0.0111 0.880
DEMetro_Z_vs_SMC 0.3 2.756 0.0187 0.796
DEMetro_Z_vs_SMC 0.5 2.870 0.0152 0.828
DEMetro_Z_vs_SMC 0.9 1.323 0.213 0.382
DEMetro_Z_vs_SMC 0.95 0.440 0.668 0.127
DEMetro_Z_vs_SMC 0.99 1.745 0.109 0.504
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.036 0.030 0.013 0.462
HMC 0.3 0.032 0.029 0.015 0.151
HMC 0.5 0.031 0.021 0.013 0.716
HMC 0.9 0.051 0.028 0.018 1.296
HMC 0.95 0.062 0.021 0.020 2.010
HMC 0.99 0.023 0.037 0.018 -0.798
SMC 0.0 0.028 0.030 0.013 -0.121
SMC 0.3 0.024 0.029 0.015 -0.339
SMC 0.5 0.018 0.021 0.013 -0.214
SMC 0.9 0.032 0.028 0.018 0.191
SMC 0.95 0.029 0.021 0.020 0.394
SMC 0.99 0.024 0.037 0.018 -0.758
Metro 0.0 0.049 0.030 0.013 1.442
Metro 0.3 0.058 0.029 0.015 1.917
Metro 0.5 0.044 0.021 0.013 1.668
Metro 0.9 0.057 0.028 0.018 1.630
Metro 0.95 0.142 0.021 0.020 6.019
Metro 0.99 0.234 0.037 0.018 11.062
DEMetro_Z 0.0 0.055 0.030 0.013 1.877
DEMetro_Z 0.3 0.050 0.029 0.015 1.407
DEMetro_Z 0.5 0.046 0.021 0.013 1.844
DEMetro_Z 0.9 0.054 0.028 0.018 1.445
DEMetro_Z 0.95 0.034 0.021 0.020 0.660
DEMetro_Z 0.99 0.046 0.037 0.018 0.491
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -2.926 0.00782 -1.183
HMC 0.3 0.082 0.935 0.033
HMC 0.5 2.109 0.048 1.071
HMC 0.9 2.218 0.0379 1.048
HMC 0.95 3.001 0.00668 1.323
HMC 0.99 1.701 0.109 1.182
SMC 0.0 -2.996 0.00716 -1.484
SMC 0.3 -0.172 0.865 -0.080
SMC 0.5 -0.416 0.682 -0.190
SMC 0.9 0.208 0.838 0.109
SMC 0.95 -0.368 0.717 -0.130
SMC 0.99 -0.545 0.592 -0.200
Metro 0.0 3.305 0.00509 2.623
Metro 0.3 4.205 0.000444 2.104
Metro 0.5 3.267 0.00435 1.865
Metro 0.9 3.736 0.00293 5.818
Metro 0.95 6.908 2.07e-05 13.862
Metro 0.99 6.278 5.75e-05 25.295
DEMetro_Z 0.0 3.798 0.00253 5.205
DEMetro_Z 0.3 4.776 0.000384 5.100
DEMetro_Z 0.5 6.921 1.38e-06 3.660
DEMetro_Z 0.9 3.058 0.00901 2.906
DEMetro_Z 0.95 4.239 0.000588 2.664
DEMetro_Z 0.99 6.471 3.95e-06 3.545
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -2.226 0.0479 -0.642
Metro_vs_DEMetro_Z 0.3 -2.678 0.0215 -0.773
Metro_vs_DEMetro_Z 0.5 -2.172 0.0526 -0.627
Metro_vs_DEMetro_Z 0.9 1.703 0.117 0.492
Metro_vs_DEMetro_Z 0.95 5.117 0.000335 1.477
Metro_vs_DEMetro_Z 0.99 5.418 0.000211 1.564
DEMetro_Z_vs_SMC 0.0 5.386 0.000221 1.555
DEMetro_Z_vs_SMC 0.3 4.474 0.00094 1.292
DEMetro_Z_vs_SMC 0.5 6.754 3.14e-05 1.950
DEMetro_Z_vs_SMC 0.9 2.777 0.018 0.802
DEMetro_Z_vs_SMC 0.95 6.409 5.01e-05 1.850
DEMetro_Z_vs_SMC 0.99 10.563 4.27e-07 3.049
HMC_vs_DEMetro_Z 0.0 -4.405 0.00105 -1.272
HMC_vs_DEMetro_Z 0.3 -4.402 0.00106 -1.271
HMC_vs_DEMetro_Z 0.5 -3.819 0.00285 -1.103
HMC_vs_DEMetro_Z 0.9 -1.779 0.103 -0.514
HMC_vs_DEMetro_Z 0.95 -1.981 0.0731 -0.572
HMC_vs_DEMetro_Z 0.99 -2.966 0.0128 -0.856
HMC_vs_Metro 0.0 -4.823 0.000533 -1.392
HMC_vs_Metro 0.3 -4.132 0.00167 -1.193
HMC_vs_Metro 0.5 -1.632 0.131 -0.471
HMC_vs_Metro 0.9 -2.786 0.0177 -0.804
HMC_vs_Metro 0.95 -6.103 7.7e-05 -1.762
HMC_vs_Metro 0.99 -6.167 7.03e-05 -1.780
HMC_vs_SMC 0.0 0.817 0.432 0.236
HMC_vs_SMC 0.3 0.300 0.77 0.086
HMC_vs_SMC 0.5 2.528 0.0281 0.730
HMC_vs_SMC 0.9 1.546 0.15 0.446
HMC_vs_SMC 0.95 3.473 0.00522 1.002
HMC_vs_SMC 0.99 1.957 0.0762 0.565
Metro_vs_SMC 0.0 5.465 0.000196 1.577
Metro_vs_SMC 0.3 3.834 0.00278 1.107
Metro_vs_SMC 0.5 3.136 0.00947 0.905
Metro_vs_SMC 0.9 3.264 0.00754 0.942
Metro_vs_SMC 0.95 7.119 1.94e-05 2.055
Metro_vs_SMC 0.99 6.327 5.62e-05 1.827
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.027 0.032 0.004 -1.183
HMC 0.3 0.029 0.029 0.007 0.033
HMC 0.5 0.035 0.028 0.006 1.071
HMC 0.9 0.037 0.027 0.009 1.048
HMC 0.95 0.037 0.026 0.009 1.323
HMC 0.99 0.038 0.027 0.009 1.182
SMC 0.0 0.026 0.032 0.004 -1.484
SMC 0.3 0.029 0.029 0.007 -0.080
SMC 0.5 0.027 0.028 0.006 -0.190
SMC 0.9 0.028 0.027 0.009 0.109
SMC 0.95 0.024 0.026 0.009 -0.130
SMC 0.99 0.026 0.027 0.009 -0.200
Metro 0.0 0.043 0.032 0.004 2.623
Metro 0.3 0.043 0.029 0.007 2.104
Metro 0.5 0.040 0.028 0.006 1.865
Metro 0.9 0.078 0.027 0.009 5.818
Metro 0.95 0.144 0.026 0.009 13.862
Metro 0.99 0.253 0.027 0.009 25.295
DEMetro_Z 0.0 0.054 0.032 0.004 5.205
DEMetro_Z 0.3 0.064 0.029 0.007 5.100
DEMetro_Z 0.5 0.051 0.028 0.006 3.660
DEMetro_Z 0.9 0.053 0.027 0.009 2.906
DEMetro_Z 0.95 0.048 0.026 0.009 2.664
DEMetro_Z 0.99 0.059 0.027 0.009 3.545
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -2.392 0.0265 -0.864
HMC 0.3 0.234 0.817 0.096
HMC 0.5 2.115 0.0517 1.555
HMC 0.9 2.500 0.0219 1.333
HMC 0.95 2.833 0.00972 1.204
HMC 0.99 1.327 0.202 0.802
SMC 0.0 -2.966 0.00713 -1.211
SMC 0.3 -0.576 0.571 -0.276
SMC 0.5 -0.594 0.56 -0.377
SMC 0.9 0.486 0.633 0.262
SMC 0.95 -0.735 0.471 -0.267
SMC 0.99 -1.132 0.27 -0.429
Metro 0.0 3.007 0.00763 1.709
Metro 0.3 3.602 0.00171 1.711
Metro 0.5 3.394 0.00405 2.495
Metro 0.9 4.915 0.000325 5.812
Metro 0.95 8.560 1.92e-06 12.138
Metro 0.99 7.762 7.57e-06 20.918
DEMetro_Z 0.0 2.867 0.0137 3.290
DEMetro_Z 0.3 3.805 0.00223 3.932
DEMetro_Z 0.5 5.411 0.000118 5.354
DEMetro_Z 0.9 3.248 0.00602 2.855
DEMetro_Z 0.95 4.159 0.000582 2.315
DEMetro_Z 0.99 4.893 0.000135 2.931
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 4.115 0.00171 1.188
DEMetro_Z_vs_SMC 0.3 3.707 0.00346 1.070
DEMetro_Z_vs_SMC 0.5 5.626 0.000154 1.624
DEMetro_Z_vs_SMC 0.9 2.725 0.0198 0.787
DEMetro_Z_vs_SMC 0.95 5.703 0.000138 1.646
DEMetro_Z_vs_SMC 0.99 7.808 8.22e-06 2.254
HMC_vs_Metro 0.0 -5.204 0.000293 -1.502
HMC_vs_Metro 0.3 -3.570 0.0044 -1.031
HMC_vs_Metro 0.5 -1.129 0.283 -0.326
HMC_vs_Metro 0.9 -3.367 0.00629 -0.972
HMC_vs_Metro 0.95 -7.382 1.39e-05 -2.131
HMC_vs_Metro 0.99 -7.698 9.4e-06 -2.222
Metro_vs_DEMetro_Z 0.0 -1.517 0.157 -0.438
Metro_vs_DEMetro_Z 0.3 -1.902 0.0836 -0.549
Metro_vs_DEMetro_Z 0.5 -2.023 0.0681 -0.584
Metro_vs_DEMetro_Z 0.9 2.401 0.0351 0.693
Metro_vs_DEMetro_Z 0.95 5.959 9.47e-05 1.720
Metro_vs_DEMetro_Z 0.99 6.772 3.06e-05 1.955
HMC_vs_SMC 0.0 1.181 0.263 0.341
HMC_vs_SMC 0.3 1.047 0.318 0.302
HMC_vs_SMC 0.5 2.425 0.0337 0.700
HMC_vs_SMC 0.9 1.685 0.12 0.487
HMC_vs_SMC 0.95 3.744 0.00324 1.081
HMC_vs_SMC 0.99 1.955 0.0765 0.564
Metro_vs_SMC 0.0 5.046 0.000375 1.457
Metro_vs_SMC 0.3 3.587 0.00426 1.036
Metro_vs_SMC 0.5 2.986 0.0124 0.862
Metro_vs_SMC 0.9 4.237 0.0014 1.223
Metro_vs_SMC 0.95 9.130 1.82e-06 2.636
Metro_vs_SMC 0.99 7.655 9.9e-06 2.210
HMC_vs_DEMetro_Z 0.0 -3.434 0.00558 -0.991
HMC_vs_DEMetro_Z 0.3 -3.314 0.0069 -0.957
HMC_vs_DEMetro_Z 0.5 -3.334 0.00667 -0.962
HMC_vs_DEMetro_Z 0.9 -1.649 0.127 -0.476
HMC_vs_DEMetro_Z 0.95 -1.923 0.0807 -0.555
HMC_vs_DEMetro_Z 0.99 -2.878 0.015 -0.831
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.013 0.016 0.004 -0.864
HMC 0.3 0.015 0.014 0.005 0.096
HMC 0.5 0.018 0.014 0.003 1.555
HMC 0.9 0.021 0.014 0.005 1.333
HMC 0.95 0.021 0.014 0.005 1.204
HMC 0.99 0.020 0.015 0.005 0.802
SMC 0.0 0.012 0.016 0.004 -1.211
SMC 0.3 0.013 0.014 0.005 -0.276
SMC 0.5 0.013 0.014 0.003 -0.377
SMC 0.9 0.015 0.014 0.005 0.262
SMC 0.95 0.013 0.014 0.005 -0.267
SMC 0.99 0.013 0.015 0.005 -0.429
Metro 0.0 0.022 0.016 0.004 1.709
Metro 0.3 0.022 0.014 0.005 1.711
Metro 0.5 0.020 0.014 0.003 2.495
Metro 0.9 0.045 0.014 0.005 5.812
Metro 0.95 0.079 0.014 0.005 12.138
Metro 0.99 0.130 0.015 0.005 20.918
DEMetro_Z 0.0 0.028 0.016 0.004 3.290
DEMetro_Z 0.3 0.033 0.014 0.005 3.932
DEMetro_Z 0.5 0.028 0.014 0.003 5.354
DEMetro_Z 0.9 0.029 0.014 0.005 2.855
DEMetro_Z 0.95 0.027 0.014 0.005 2.315
DEMetro_Z 0.99 0.032 0.015 0.005 2.931
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.858 0.4 -0.351
HMC 0.3 -0.726 0.476 -0.267
HMC 0.5 -0.340 0.738 -0.161
HMC 0.9 -0.326 0.748 -0.149
HMC 0.95 1.462 0.166 1.196
HMC 0.99 1.930 0.0672 0.886
SMC 0.0 -1.006 0.326 -0.494
SMC 0.3 -0.460 0.65 -0.188
SMC 0.5 -0.301 0.766 -0.124
SMC 0.9 -0.061 0.952 -0.030
SMC 0.95 0.901 0.378 0.421
SMC 0.99 0.049 0.961 0.019
Metro 0.0 2.132 0.0501 1.574
Metro 0.3 3.047 0.00784 2.061
Metro 0.5 1.401 0.183 1.132
Metro 0.9 4.592 0.000549 5.095
Metro 0.95 3.233 0.00761 6.764
Metro 0.99 5.860 0.000105 24.862
DEMetro_Z 0.0 1.607 0.128 1.077
DEMetro_Z 0.3 1.630 0.122 1.041
DEMetro_Z 0.5 2.395 0.0309 1.909
DEMetro_Z 0.9 2.256 0.0391 1.586
DEMetro_Z 0.95 1.947 0.0744 2.244
DEMetro_Z 0.99 1.361 0.189 0.704
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -2.043 0.0657 -0.590
HMC_vs_DEMetro_Z 0.3 -1.817 0.0966 -0.524
HMC_vs_DEMetro_Z 0.5 -2.846 0.0159 -0.822
HMC_vs_DEMetro_Z 0.9 -2.371 0.0371 -0.684
HMC_vs_DEMetro_Z 0.95 -0.764 0.461 -0.221
HMC_vs_DEMetro_Z 0.99 0.297 0.772 0.086
Metro_vs_SMC 0.0 3.702 0.00349 1.069
Metro_vs_SMC 0.3 3.252 0.00771 0.939
Metro_vs_SMC 0.5 2.053 0.0646 0.593
Metro_vs_SMC 0.9 5.125 0.000331 1.479
Metro_vs_SMC 0.95 3.037 0.0113 0.877
Metro_vs_SMC 0.99 6.041 8.41e-05 1.744
Metro_vs_DEMetro_Z 0.0 0.469 0.649 0.135
Metro_vs_DEMetro_Z 0.3 1.199 0.256 0.346
Metro_vs_DEMetro_Z 0.5 -0.743 0.473 -0.214
Metro_vs_DEMetro_Z 0.9 3.422 0.0057 0.988
Metro_vs_DEMetro_Z 0.95 1.691 0.119 0.488
Metro_vs_DEMetro_Z 0.99 5.795 0.00012 1.673
HMC_vs_Metro 0.0 -3.184 0.0087 -0.919
HMC_vs_Metro 0.3 -3.514 0.00485 -1.014
HMC_vs_Metro 0.5 -1.612 0.135 -0.465
HMC_vs_Metro 0.9 -4.283 0.00129 -1.236
HMC_vs_Metro 0.95 -2.312 0.0412 -0.667
HMC_vs_Metro 0.99 -5.487 0.00019 -1.584
HMC_vs_SMC 0.0 0.444 0.666 0.128
HMC_vs_SMC 0.3 -0.225 0.826 -0.065
HMC_vs_SMC 0.5 -0.087 0.932 -0.025
HMC_vs_SMC 0.9 -0.210 0.837 -0.061
HMC_vs_SMC 0.95 1.332 0.21 0.385
HMC_vs_SMC 0.99 1.814 0.097 0.524
DEMetro_Z_vs_SMC 0.0 2.139 0.0557 0.618
DEMetro_Z_vs_SMC 0.3 2.154 0.0543 0.622
DEMetro_Z_vs_SMC 0.5 2.293 0.0426 0.662
DEMetro_Z_vs_SMC 0.9 2.570 0.026 0.742
DEMetro_Z_vs_SMC 0.95 1.489 0.165 0.430
DEMetro_Z_vs_SMC 0.99 1.303 0.219 0.376
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.022 0.025 0.008 -0.351
HMC 0.3 0.018 0.020 0.009 -0.267
HMC 0.5 0.022 0.024 0.010 -0.161
HMC 0.9 0.017 0.019 0.014 -0.149
HMC 0.95 0.031 0.017 0.012 1.196
HMC 0.99 0.032 0.018 0.016 0.886
SMC 0.0 0.021 0.025 0.008 -0.494
SMC 0.3 0.019 0.020 0.009 -0.188
SMC 0.5 0.023 0.024 0.010 -0.124
SMC 0.9 0.019 0.019 0.014 -0.030
SMC 0.95 0.022 0.017 0.012 0.421
SMC 0.99 0.018 0.018 0.016 0.019
Metro 0.0 0.038 0.025 0.008 1.574
Metro 0.3 0.040 0.020 0.009 2.061
Metro 0.5 0.035 0.024 0.010 1.132
Metro 0.9 0.089 0.019 0.014 5.095
Metro 0.95 0.096 0.017 0.012 6.764
Metro 0.99 0.407 0.018 0.016 24.862
DEMetro_Z 0.0 0.034 0.025 0.008 1.077
DEMetro_Z 0.3 0.030 0.020 0.009 1.041
DEMetro_Z 0.5 0.042 0.024 0.010 1.909
DEMetro_Z 0.9 0.041 0.019 0.014 1.586
DEMetro_Z 0.95 0.043 0.017 0.012 2.244
DEMetro_Z 0.99 0.029 0.018 0.016 0.704
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 0.761 0.455 0.368
HMC 0.3 0.058 0.955 0.022
HMC 0.5 0.225 0.824 0.098
HMC 0.9 1.975 0.0666 1.388
HMC 0.95 2.033 0.0572 1.145
HMC 0.99 -0.523 0.607 -0.272
SMC 0.0 -0.114 0.911 -0.050
SMC 0.3 0.639 0.529 0.248
SMC 0.5 2.338 0.0303 1.205
SMC 0.9 -1.770 0.0923 -0.623
SMC 0.95 1.288 0.211 0.507
SMC 0.99 -2.291 0.0319 -0.908
Metro 0.0 2.006 0.0611 1.210
Metro 0.3 0.780 0.446 0.457
Metro 0.5 2.567 0.0223 2.098
Metro 0.9 3.087 0.00642 1.756
Metro 0.95 5.391 0.00014 6.083
Metro 0.99 4.522 0.000826 12.858
DEMetro_Z 0.0 3.678 0.00249 3.046
DEMetro_Z 0.3 2.219 0.041 1.415
DEMetro_Z 0.5 4.867 0.000147 2.958
DEMetro_Z 0.9 2.472 0.0259 1.804
DEMetro_Z 0.95 2.293 0.0368 1.681
DEMetro_Z 0.99 0.849 0.408 0.508
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 0.824 0.427 0.238
HMC_vs_SMC 0.3 -0.539 0.601 -0.155
HMC_vs_SMC 0.5 -1.903 0.0836 -0.549
HMC_vs_SMC 0.9 2.762 0.0185 0.797
HMC_vs_SMC 0.95 1.391 0.192 0.402
HMC_vs_SMC 0.99 1.499 0.162 0.433
Metro_vs_DEMetro_Z 0.0 -2.069 0.0628 -0.597
Metro_vs_DEMetro_Z 0.3 -1.020 0.33 -0.294
Metro_vs_DEMetro_Z 0.5 -1.076 0.305 -0.311
Metro_vs_DEMetro_Z 0.9 -0.092 0.928 -0.027
Metro_vs_DEMetro_Z 0.95 3.059 0.0109 0.883
Metro_vs_DEMetro_Z 0.99 4.270 0.00132 1.233
HMC_vs_Metro 0.0 -1.147 0.276 -0.331
HMC_vs_Metro 0.3 -0.857 0.41 -0.247
HMC_vs_Metro 0.5 -2.278 0.0437 -0.658
HMC_vs_Metro 0.9 -0.565 0.584 -0.163
HMC_vs_Metro 0.95 -4.368 0.00112 -1.261
HMC_vs_Metro 0.99 -4.666 0.000687 -1.347
HMC_vs_DEMetro_Z 0.0 -3.351 0.00647 -0.967
HMC_vs_DEMetro_Z 0.3 -2.362 0.0377 -0.682
HMC_vs_DEMetro_Z 0.5 -4.492 0.000913 -1.297
HMC_vs_DEMetro_Z 0.9 -0.458 0.656 -0.132
HMC_vs_DEMetro_Z 0.95 -0.749 0.469 -0.216
HMC_vs_DEMetro_Z 0.99 -1.071 0.307 -0.309
Metro_vs_SMC 0.0 1.762 0.106 0.509
Metro_vs_SMC 0.3 0.419 0.683 0.121
Metro_vs_SMC 0.5 1.147 0.276 0.331
Metro_vs_SMC 0.9 4.033 0.00197 1.164
Metro_vs_SMC 0.95 5.240 0.000277 1.513
Metro_vs_SMC 0.99 4.689 0.000662 1.354
DEMetro_Z_vs_SMC 0.0 3.502 0.00495 1.011
DEMetro_Z_vs_SMC 0.3 1.854 0.0907 0.535
DEMetro_Z_vs_SMC 0.5 2.356 0.038 0.680
DEMetro_Z_vs_SMC 0.9 3.355 0.00642 0.969
DEMetro_Z_vs_SMC 0.95 1.680 0.121 0.485
DEMetro_Z_vs_SMC 0.99 2.169 0.0529 0.626
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.035 0.030 0.013 0.368
HMC 0.3 0.030 0.029 0.015 0.022
HMC 0.5 0.023 0.021 0.013 0.098
HMC 0.9 0.053 0.028 0.018 1.388
HMC 0.95 0.044 0.021 0.020 1.145
HMC 0.99 0.033 0.037 0.018 -0.272
SMC 0.0 0.029 0.030 0.013 -0.050
SMC 0.3 0.033 0.029 0.015 0.248
SMC 0.5 0.037 0.021 0.013 1.205
SMC 0.9 0.017 0.028 0.018 -0.623
SMC 0.95 0.031 0.021 0.020 0.507
SMC 0.99 0.021 0.037 0.018 -0.908
Metro 0.0 0.046 0.030 0.013 1.210
Metro 0.3 0.036 0.029 0.015 0.457
Metro 0.5 0.049 0.021 0.013 2.098
Metro 0.9 0.059 0.028 0.018 1.756
Metro 0.95 0.144 0.021 0.020 6.083
Metro 0.99 0.266 0.037 0.018 12.858
DEMetro_Z 0.0 0.070 0.030 0.013 3.046
DEMetro_Z 0.3 0.050 0.029 0.015 1.415
DEMetro_Z 0.5 0.061 0.021 0.013 2.958
DEMetro_Z 0.9 0.060 0.028 0.018 1.804
DEMetro_Z 0.95 0.055 0.021 0.020 1.681
DEMetro_Z 0.99 0.046 0.037 0.018 0.508
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.551 0.588 -0.274
HMC 0.3 -0.352 0.728 -0.125
HMC 0.5 0.692 0.496 0.289
HMC 0.9 1.398 0.179 0.753
HMC 0.95 2.046 0.0611 1.926
HMC 0.99 2.583 0.0176 1.246
SMC 0.0 -1.021 0.321 -0.583
SMC 0.3 -0.521 0.607 -0.198
SMC 0.5 0.448 0.659 0.207
SMC 0.9 -0.163 0.872 -0.084
SMC 0.95 0.759 0.456 0.329
SMC 0.99 -0.478 0.637 -0.177
Metro 0.0 4.386 0.000497 3.025
Metro 0.3 4.243 0.000538 2.527
Metro 0.5 3.125 0.008 3.047
Metro 0.9 5.081 0.000273 7.149
Metro 0.95 5.438 0.000173 10.155
Metro 0.99 7.201 1.7e-05 42.055
DEMetro_Z 0.0 5.503 0.000101 5.459
DEMetro_Z 0.3 4.286 0.000495 2.572
DEMetro_Z 0.5 5.511 6.92e-05 4.297
DEMetro_Z 0.9 4.905 0.000138 3.008
DEMetro_Z 0.95 3.433 0.00462 3.757
DEMetro_Z 0.99 2.719 0.0152 1.788
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -1.940 0.0784 -0.560
Metro_vs_DEMetro_Z 0.3 -0.060 0.953 -0.017
Metro_vs_DEMetro_Z 0.5 -0.981 0.348 -0.283
Metro_vs_DEMetro_Z 0.9 3.142 0.00937 0.907
Metro_vs_DEMetro_Z 0.95 2.893 0.0146 0.835
Metro_vs_DEMetro_Z 0.99 6.832 2.83e-05 1.972
DEMetro_Z_vs_SMC 0.0 5.112 0.000338 1.476
DEMetro_Z_vs_SMC 0.3 5.701 0.000138 1.646
DEMetro_Z_vs_SMC 0.5 4.584 0.000785 1.323
DEMetro_Z_vs_SMC 0.9 4.850 0.000511 1.400
DEMetro_Z_vs_SMC 0.95 3.159 0.0091 0.912
DEMetro_Z_vs_SMC 0.99 2.669 0.0218 0.770
HMC_vs_DEMetro_Z 0.0 -5.175 0.000306 -1.494
HMC_vs_DEMetro_Z 0.3 -4.287 0.00128 -1.238
HMC_vs_DEMetro_Z 0.5 -5.421 0.00021 -1.565
HMC_vs_DEMetro_Z 0.9 -4.440 0.000995 -1.282
HMC_vs_DEMetro_Z 0.95 -1.352 0.203 -0.390
HMC_vs_DEMetro_Z 0.99 -0.757 0.465 -0.218
HMC_vs_Metro 0.0 -4.803 0.000551 -1.387
HMC_vs_Metro 0.3 -5.287 0.000258 -1.526
HMC_vs_Metro 0.5 -2.949 0.0132 -0.851
HMC_vs_Metro 0.9 -4.364 0.00113 -1.260
HMC_vs_Metro 0.95 -3.937 0.00232 -1.136
HMC_vs_Metro 0.99 -6.917 2.53e-05 -1.997
HMC_vs_SMC 0.0 0.595 0.564 0.172
HMC_vs_SMC 0.3 0.211 0.837 0.061
HMC_vs_SMC 0.5 0.216 0.833 0.062
HMC_vs_SMC 0.9 1.499 0.162 0.433
HMC_vs_SMC 0.95 2.226 0.0479 0.642
HMC_vs_SMC 0.99 2.845 0.016 0.821
Metro_vs_SMC 0.0 9.507 1.22e-06 2.744
Metro_vs_SMC 0.3 4.832 0.000526 1.395
Metro_vs_SMC 0.5 3.299 0.00709 0.952
Metro_vs_SMC 0.9 5.331 0.000241 1.539
Metro_vs_SMC 0.95 5.561 0.00017 1.605
Metro_vs_SMC 0.99 7.346 1.46e-05 2.121
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.031 0.032 0.004 -0.274
HMC 0.3 0.028 0.029 0.007 -0.125
HMC 0.5 0.030 0.028 0.006 0.289
HMC 0.9 0.034 0.027 0.009 0.753
HMC 0.95 0.042 0.026 0.009 1.926
HMC 0.99 0.039 0.027 0.009 1.246
SMC 0.0 0.030 0.032 0.004 -0.583
SMC 0.3 0.028 0.029 0.007 -0.198
SMC 0.5 0.030 0.028 0.006 0.207
SMC 0.9 0.027 0.027 0.009 -0.084
SMC 0.95 0.028 0.026 0.009 0.329
SMC 0.99 0.026 0.027 0.009 -0.177
Metro 0.0 0.045 0.032 0.004 3.025
Metro 0.3 0.046 0.029 0.007 2.527
Metro 0.5 0.047 0.028 0.006 3.047
Metro 0.9 0.090 0.027 0.009 7.149
Metro 0.95 0.112 0.026 0.009 10.155
Metro 0.99 0.402 0.027 0.009 42.055
DEMetro_Z 0.0 0.055 0.032 0.004 5.459
DEMetro_Z 0.3 0.047 0.029 0.007 2.572
DEMetro_Z 0.5 0.055 0.028 0.006 4.297
DEMetro_Z 0.9 0.054 0.027 0.009 3.008
DEMetro_Z 0.95 0.058 0.026 0.009 3.757
DEMetro_Z 0.99 0.043 0.027 0.009 1.788
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.575 0.571 -0.257
HMC 0.3 -0.766 0.452 -0.272
HMC 0.5 0.858 0.402 0.477
HMC 0.9 1.591 0.132 1.064
HMC 0.95 1.761 0.1 1.436
HMC 0.99 1.629 0.118 0.686
SMC 0.0 -0.763 0.454 -0.368
SMC 0.3 -1.007 0.325 -0.392
SMC 0.5 1.010 0.329 0.787
SMC 0.9 0.064 0.949 0.032
SMC 0.95 0.302 0.766 0.139
SMC 0.99 -1.619 0.124 -0.536
Metro 0.0 2.837 0.0121 1.911
Metro 0.3 3.572 0.00227 2.084
Metro 0.5 3.233 0.00727 4.776
Metro 0.9 5.715 7.37e-05 5.862
Metro 0.95 5.909 7.43e-05 8.642
Metro 0.99 7.100 1.93e-05 36.245
DEMetro_Z 0.0 4.305 0.000663 3.272
DEMetro_Z 0.3 3.044 0.00687 1.671
DEMetro_Z 0.5 5.929 4.32e-05 5.365
DEMetro_Z 0.9 4.740 0.000234 3.202
DEMetro_Z 0.95 3.102 0.00771 2.497
DEMetro_Z 0.99 2.317 0.0335 1.430
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 4.091 0.00179 1.181
DEMetro_Z_vs_SMC 0.3 4.124 0.00169 1.191
DEMetro_Z_vs_SMC 0.5 3.476 0.00518 1.004
DEMetro_Z_vs_SMC 0.9 4.523 0.000868 1.306
DEMetro_Z_vs_SMC 0.95 2.927 0.0138 0.845
DEMetro_Z_vs_SMC 0.99 2.952 0.0132 0.852
HMC_vs_Metro 0.0 -3.266 0.00752 -0.943
HMC_vs_Metro 0.3 -5.411 0.000213 -1.562
HMC_vs_Metro 0.5 -3.335 0.00665 -0.963
HMC_vs_Metro 0.9 -4.795 0.000558 -1.384
HMC_vs_Metro 0.95 -4.507 0.000891 -1.301
HMC_vs_Metro 0.99 -7.057 2.11e-05 -2.037
Metro_vs_DEMetro_Z 0.0 -1.591 0.14 -0.459
Metro_vs_DEMetro_Z 0.3 0.548 0.595 0.158
Metro_vs_DEMetro_Z 0.5 -0.302 0.768 -0.087
Metro_vs_DEMetro_Z 0.9 2.858 0.0156 0.825
Metro_vs_DEMetro_Z 0.95 4.004 0.00207 1.156
Metro_vs_DEMetro_Z 0.99 6.750 3.16e-05 1.948
HMC_vs_SMC 0.0 0.292 0.776 0.084
HMC_vs_SMC 0.3 0.355 0.729 0.103
HMC_vs_SMC 0.5 -0.506 0.623 -0.146
HMC_vs_SMC 0.9 1.550 0.149 0.448
HMC_vs_SMC 0.95 1.750 0.108 0.505
HMC_vs_SMC 0.99 3.100 0.0101 0.895
Metro_vs_SMC 0.0 5.374 0.000225 1.551
Metro_vs_SMC 0.3 4.296 0.00126 1.240
Metro_vs_SMC 0.5 3.418 0.00574 0.987
Metro_vs_SMC 0.9 6.664 3.54e-05 1.924
Metro_vs_SMC 0.95 6.156 7.15e-05 1.777
Metro_vs_SMC 0.99 7.204 1.74e-05 2.079
HMC_vs_DEMetro_Z 0.0 -4.274 0.00131 -1.234
HMC_vs_DEMetro_Z 0.3 -3.660 0.00375 -1.057
HMC_vs_DEMetro_Z 0.5 -4.838 0.000521 -1.397
HMC_vs_DEMetro_Z 0.9 -4.851 0.00051 -1.400
HMC_vs_DEMetro_Z 0.95 -0.997 0.34 -0.288
HMC_vs_DEMetro_Z 0.99 -1.129 0.283 -0.326
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.015 0.016 0.004 -0.257
HMC 0.3 0.013 0.014 0.005 -0.272
HMC 0.5 0.015 0.014 0.003 0.477
HMC 0.9 0.019 0.014 0.005 1.064
HMC 0.95 0.022 0.014 0.005 1.436
HMC 0.99 0.019 0.015 0.005 0.686
SMC 0.0 0.015 0.016 0.004 -0.368
SMC 0.3 0.013 0.014 0.005 -0.392
SMC 0.5 0.016 0.014 0.003 0.787
SMC 0.9 0.014 0.014 0.005 0.032
SMC 0.95 0.015 0.014 0.005 0.139
SMC 0.99 0.013 0.015 0.005 -0.536
Metro 0.0 0.023 0.016 0.004 1.911
Metro 0.3 0.024 0.014 0.005 2.084
Metro 0.5 0.026 0.014 0.003 4.776
Metro 0.9 0.045 0.014 0.005 5.862
Metro 0.95 0.061 0.014 0.005 8.642
Metro 0.99 0.214 0.015 0.005 36.245
DEMetro_Z 0.0 0.028 0.016 0.004 3.272
DEMetro_Z 0.3 0.022 0.014 0.005 1.671
DEMetro_Z 0.5 0.028 0.014 0.003 5.365
DEMetro_Z 0.9 0.031 0.014 0.005 3.202
DEMetro_Z 0.95 0.028 0.014 0.005 2.497
DEMetro_Z 0.99 0.023 0.015 0.005 1.430
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
0.0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.9 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.95 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.99 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0.0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.9 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.95 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.99 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.95
0.99
Chain
0.0
0.3
0.5
0.9
0.95
0.99

Vary_only_Dimension (MvNormal, dimension, 12 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -1.392 0.178 -0.556
HMC 5 -1.049 0.306 -0.435
HMC 8 -0.261 0.797 -0.088
HMC 12 -2.977 0.0071 -1.338
HMC 15 -0.987 0.336 -0.538
HMC 30 -2.710 0.0136 -0.956
SMC 2 -2.007 0.0579 -0.741
SMC 5 0.360 0.723 0.204
SMC 8 -0.818 0.425 -0.268
SMC 12 -0.607 0.552 -0.359
SMC 15 0.247 0.808 0.088
SMC 30 0.412 0.684 0.164
Metro 2 0.128 0.9 0.091
Metro 5 4.997 9.87e-05 2.872
Metro 8 4.003 0.000623 1.781
Metro 12 5.230 6.44e-05 3.090
Metro 15 7.236 1.52e-06 4.457
Metro 30 9.552 6.63e-09 4.701
DEMetro_Z 2 2.581 0.0222 2.283
DEMetro_Z 5 6.378 5.24e-05 419.458
DEMetro_Z 8 9.786 9.17e-07 490.906
DEMetro_Z 12 16.450 4.3e-09 1538.586
DEMetro_Z 15 19.378 7.5e-10 1641.248
DEMetro_Z 30 22.188 1.75e-10 1685.553
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -3.479 0.00516 -1.004
HMC_vs_DEMetro_Z 1 -6.394 5.12e-05 -1.846
HMC_vs_DEMetro_Z 2 -9.795 9.09e-07 -2.828
HMC_vs_DEMetro_Z 3 -16.454 4.29e-09 -4.750
HMC_vs_DEMetro_Z 4 -19.348 7.62e-10 -5.585
HMC_vs_DEMetro_Z 5 -22.208 1.73e-10 -6.411
Metro_vs_SMC 0 1.213 0.251 0.350
Metro_vs_SMC 1 3.859 0.00266 1.114
Metro_vs_SMC 2 6.401 5.07e-05 1.848
Metro_vs_SMC 3 6.547 4.15e-05 1.890
Metro_vs_SMC 4 8.113 5.72e-06 2.342
Metro_vs_SMC 5 15.417 8.54e-09 4.450
Metro_vs_DEMetro_Z 0 -1.939 0.0786 -0.560
Metro_vs_DEMetro_Z 1 -6.339 5.53e-05 -1.830
Metro_vs_DEMetro_Z 2 -9.773 9.3e-07 -2.821
Metro_vs_DEMetro_Z 3 -16.425 4.37e-09 -4.742
Metro_vs_DEMetro_Z 4 -19.319 7.75e-10 -5.577
Metro_vs_DEMetro_Z 5 -22.140 1.79e-10 -6.391
HMC_vs_Metro 0 -0.963 0.356 -0.278
HMC_vs_Metro 1 -6.211 6.61e-05 -1.793
HMC_vs_Metro 2 -5.477 0.000193 -1.581
HMC_vs_Metro 3 -9.276 1.56e-06 -2.678
HMC_vs_Metro 4 -7.813 8.18e-06 -2.255
HMC_vs_Metro 5 -10.439 4.81e-07 -3.013
HMC_vs_SMC 0 0.574 0.577 0.166
HMC_vs_SMC 1 -1.293 0.223 -0.373
HMC_vs_SMC 2 0.862 0.407 0.249
HMC_vs_SMC 3 -2.358 0.0379 -0.681
HMC_vs_SMC 4 -1.342 0.207 -0.387
HMC_vs_SMC 5 -2.912 0.0141 -0.841
DEMetro_Z_vs_SMC 0 3.576 0.00435 1.032
DEMetro_Z_vs_SMC 1 6.384 5.19e-05 1.843
DEMetro_Z_vs_SMC 2 9.799 9.06e-07 2.829
DEMetro_Z_vs_SMC 3 16.455 4.28e-09 4.750
DEMetro_Z_vs_SMC 4 19.378 7.5e-10 5.594
DEMetro_Z_vs_SMC 5 22.206 1.73e-10 6.410
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.021 0.025 0.008 -0.556
HMC 5 0.019 0.022 0.006 -0.435
HMC 8 0.020 0.021 0.009 -0.088
HMC 12 0.019 0.024 0.004 -1.338
HMC 15 0.020 0.022 0.004 -0.538
HMC 30 0.018 0.021 0.004 -0.956
SMC 2 0.019 0.025 0.008 -0.741
SMC 5 0.023 0.022 0.006 0.204
SMC 8 0.019 0.021 0.009 -0.268
SMC 12 0.023 0.024 0.004 -0.359
SMC 15 0.022 0.022 0.004 0.088
SMC 30 0.022 0.021 0.004 0.164
Metro 2 0.026 0.025 0.008 0.091
Metro 5 0.040 0.022 0.006 2.872
Metro 8 0.038 0.021 0.009 1.781
Metro 12 0.036 0.024 0.004 3.090
Metro 15 0.038 0.022 0.004 4.457
Metro 30 0.039 0.021 0.004 4.701
DEMetro_Z 2 0.044 0.025 0.008 2.283
DEMetro_Z 5 2.669 0.022 0.006 419.458
DEMetro_Z 8 4.551 0.021 0.009 490.906
DEMetro_Z 12 5.881 0.024 0.004 1538.586
DEMetro_Z 15 5.915 0.022 0.004 1641.248
DEMetro_Z 30 6.427 0.021 0.004 1685.553
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 1.686 0.108 0.863
HMC 5 1.761 0.0948 0.962
HMC 8 2.129 0.0458 1.040
HMC 12 2.982 0.00927 2.144
HMC 15 3.201 0.00558 2.105
HMC 30 5.126 0.000112 3.520
SMC 2 -0.358 0.724 -0.164
SMC 5 1.264 0.223 0.737
SMC 8 0.535 0.598 0.211
SMC 12 0.495 0.625 0.230
SMC 15 0.489 0.629 0.216
SMC 30 3.573 0.00183 1.300
Metro 2 1.770 0.0932 0.956
Metro 5 3.087 0.00734 2.146
Metro 8 4.759 0.000172 2.791
Metro 12 8.445 4.24e-07 6.073
Metro 15 8.395 7.49e-08 4.358
Metro 30 10.586 1.2e-09 5.223
DEMetro_Z 2 4.644 0.000306 3.284
DEMetro_Z 5 3.062 0.0108 6236.104
DEMetro_Z 8 9.306 1.51e-06 16249.871
DEMetro_Z 12 14.335 1.83e-08 30547.038
DEMetro_Z 15 13.021 5e-08 29793.580
DEMetro_Z 30 22.229 1.72e-10 39854.415
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 2.029 0.0674 0.586
HMC_vs_SMC 1 0.338 0.742 0.098
HMC_vs_SMC 2 2.212 0.0491 0.639
HMC_vs_SMC 3 3.380 0.00614 0.976
HMC_vs_SMC 4 2.959 0.013 0.854
HMC_vs_SMC 5 2.890 0.0147 0.834
Metro_vs_DEMetro_Z 0 -2.832 0.0163 -0.818
Metro_vs_DEMetro_Z 1 -3.061 0.0108 -0.884
Metro_vs_DEMetro_Z 2 -9.306 1.51e-06 -2.686
Metro_vs_DEMetro_Z 3 -14.333 1.84e-08 -4.138
Metro_vs_DEMetro_Z 4 -13.019 5.01e-08 -3.758
Metro_vs_DEMetro_Z 5 -22.226 1.72e-10 -6.416
HMC_vs_Metro 0 -0.207 0.84 -0.060
HMC_vs_Metro 1 -2.144 0.0552 -0.619
HMC_vs_Metro 2 -2.923 0.0139 -0.844
HMC_vs_Metro 3 -5.413 0.000212 -1.563
HMC_vs_Metro 4 -2.620 0.0238 -0.756
HMC_vs_Metro 5 -1.927 0.0802 -0.556
HMC_vs_DEMetro_Z 0 -5.236 0.000279 -1.511
HMC_vs_DEMetro_Z 1 -3.061 0.0108 -0.884
HMC_vs_DEMetro_Z 2 -9.305 1.51e-06 -2.686
HMC_vs_DEMetro_Z 3 -14.334 1.84e-08 -4.138
HMC_vs_DEMetro_Z 4 -13.021 5.01e-08 -3.759
HMC_vs_DEMetro_Z 5 -22.228 1.72e-10 -6.417
Metro_vs_SMC 0 2.599 0.0247 0.750
Metro_vs_SMC 1 1.734 0.111 0.500
Metro_vs_SMC 2 5.108 0.00034 1.475
Metro_vs_SMC 3 9.971 7.61e-07 2.878
Metro_vs_SMC 4 8.275 4.73e-06 2.389
Metro_vs_SMC 5 9.437 1.32e-06 2.724
DEMetro_Z_vs_SMC 0 4.884 0.000484 1.410
DEMetro_Z_vs_SMC 1 3.062 0.0108 0.884
DEMetro_Z_vs_SMC 2 9.307 1.51e-06 2.687
DEMetro_Z_vs_SMC 3 14.335 1.84e-08 4.138
DEMetro_Z_vs_SMC 4 13.021 5e-08 3.759
DEMetro_Z_vs_SMC 5 22.228 1.72e-10 6.417
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.041 0.030 0.013 0.863
HMC 5 0.035 0.027 0.008 0.962
HMC 8 0.036 0.028 0.008 1.040
HMC 12 0.039 0.031 0.004 2.144
HMC 15 0.042 0.032 0.005 2.105
HMC 30 0.045 0.030 0.004 3.520
SMC 2 0.028 0.030 0.013 -0.164
SMC 5 0.033 0.027 0.008 0.737
SMC 8 0.029 0.028 0.008 0.211
SMC 12 0.032 0.031 0.004 0.230
SMC 15 0.033 0.032 0.005 0.216
SMC 30 0.036 0.030 0.004 1.300
Metro 2 0.043 0.030 0.013 0.956
Metro 5 0.045 0.027 0.008 2.146
Metro 8 0.049 0.028 0.008 2.791
Metro 12 0.054 0.031 0.004 6.073
Metro 15 0.053 0.032 0.005 4.358
Metro 30 0.052 0.030 0.004 5.223
DEMetro_Z 2 0.074 0.030 0.013 3.284
DEMetro_Z 5 50.722 0.027 0.008 6236.104
DEMetro_Z 8 122.836 0.028 0.008 16249.871
DEMetro_Z 12 118.279 0.031 0.004 30547.038
DEMetro_Z 15 145.270 0.032 0.005 29793.580
DEMetro_Z 30 164.523 0.030 0.004 39854.415
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -0.824 0.419 -0.410
HMC 5 -0.182 0.857 -0.071
HMC 8 -0.275 0.787 -0.094
HMC 12 -1.457 0.159 -0.610
HMC 15 0.808 0.428 0.389
HMC 30 0.286 0.778 0.100
SMC 2 -1.820 0.0826 -0.797
SMC 5 1.085 0.29 0.486
SMC 8 -1.524 0.148 -0.484
SMC 12 -0.538 0.597 -0.285
SMC 15 1.085 0.29 0.398
SMC 30 1.042 0.309 0.435
Metro 2 2.115 0.0531 1.784
Metro 5 6.524 6.27e-06 4.142
Metro 8 4.836 9.59e-05 2.335
Metro 12 6.628 3.84e-06 3.894
Metro 15 7.137 4e-06 5.438
Metro 30 11.080 4.3e-09 6.889
DEMetro_Z 2 6.485 2.22e-05 6.806
DEMetro_Z 5 6.736 3.22e-05 1024.884
DEMetro_Z 8 16.066 5.52e-09 1398.626
DEMetro_Z 12 19.832 5.85e-10 3488.533
DEMetro_Z 15 25.152 4.52e-11 3926.191
DEMetro_Z 30 44.568 8.86e-14 5288.964
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -4.495 0.000909 -1.298
Metro_vs_DEMetro_Z 1 -6.716 3.31e-05 -1.939
Metro_vs_DEMetro_Z 2 -16.082 5.46e-09 -4.642
Metro_vs_DEMetro_Z 3 -19.813 5.91e-10 -5.719
Metro_vs_DEMetro_Z 4 -25.086 4.65e-11 -7.242
Metro_vs_DEMetro_Z 5 -44.481 9.06e-14 -12.840
DEMetro_Z_vs_SMC 0 8.377 4.2e-06 2.418
DEMetro_Z_vs_SMC 1 6.735 3.22e-05 1.944
DEMetro_Z_vs_SMC 2 16.078 5.48e-09 4.641
DEMetro_Z_vs_SMC 3 19.840 5.82e-10 5.727
DEMetro_Z_vs_SMC 4 25.149 4.52e-11 7.260
DEMetro_Z_vs_SMC 5 44.556 8.89e-14 12.862
HMC_vs_DEMetro_Z 0 -8.112 5.72e-06 -2.342
HMC_vs_DEMetro_Z 1 -6.738 3.21e-05 -1.945
HMC_vs_DEMetro_Z 2 -16.074 5.49e-09 -4.640
HMC_vs_DEMetro_Z 3 -19.838 5.83e-10 -5.727
HMC_vs_DEMetro_Z 4 -25.165 4.49e-11 -7.264
HMC_vs_DEMetro_Z 5 -44.586 8.83e-14 -12.871
HMC_vs_Metro 0 -2.716 0.0201 -0.784
HMC_vs_Metro 1 -7.571 1.1e-05 -2.186
HMC_vs_Metro 2 -6.997 2.28e-05 -2.020
HMC_vs_Metro 3 -10.845 3.27e-07 -3.131
HMC_vs_Metro 4 -6.075 8.02e-05 -1.754
HMC_vs_Metro 5 -10.768 3.51e-07 -3.108
HMC_vs_SMC 0 0.813 0.433 0.235
HMC_vs_SMC 1 -1.628 0.132 -0.470
HMC_vs_SMC 2 1.822 0.0957 0.526
HMC_vs_SMC 3 -0.800 0.441 -0.231
HMC_vs_SMC 4 -0.020 0.985 -0.006
HMC_vs_SMC 5 -0.852 0.412 -0.246
Metro_vs_SMC 0 3.205 0.00837 0.925
Metro_vs_SMC 1 5.821 0.000116 1.680
Metro_vs_SMC 2 7.819 8.11e-06 2.257
Metro_vs_SMC 3 7.715 9.21e-06 2.227
Metro_vs_SMC 4 6.937 2.46e-05 2.003
Metro_vs_SMC 5 16.799 3.44e-09 4.850
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.031 0.032 0.004 -0.410
HMC 5 0.028 0.029 0.004 -0.071
HMC 8 0.029 0.029 0.005 -0.094
HMC 12 0.028 0.030 0.003 -0.610
HMC 15 0.030 0.029 0.002 0.389
HMC 30 0.028 0.028 0.002 0.100
SMC 2 0.029 0.032 0.004 -0.797
SMC 5 0.030 0.029 0.004 0.486
SMC 8 0.027 0.029 0.005 -0.484
SMC 12 0.029 0.030 0.003 -0.285
SMC 15 0.030 0.029 0.002 0.398
SMC 30 0.029 0.028 0.002 0.435
Metro 2 0.040 0.032 0.004 1.784
Metro 5 0.045 0.029 0.004 4.142
Metro 8 0.042 0.029 0.005 2.335
Metro 12 0.040 0.030 0.003 3.894
Metro 15 0.041 0.029 0.002 5.438
Metro 30 0.041 0.028 0.002 6.889
DEMetro_Z 2 0.060 0.032 0.004 6.806
DEMetro_Z 5 4.078 0.029 0.004 1024.884
DEMetro_Z 8 7.486 0.029 0.005 1398.626
DEMetro_Z 12 8.772 0.030 0.003 3488.533
DEMetro_Z 15 9.090 0.029 0.002 3926.191
DEMetro_Z 30 10.080 0.028 0.002 5288.964
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -0.575 0.571 -0.264
HMC 5 -0.314 0.757 -0.125
HMC 8 0.257 0.8 0.088
HMC 12 -2.081 0.0498 -0.961
HMC 15 0.273 0.787 0.123
HMC 30 -0.670 0.511 -0.236
SMC 2 -1.657 0.112 -0.609
SMC 5 0.897 0.38 0.422
SMC 8 -0.981 0.341 -0.314
SMC 12 -0.683 0.503 -0.392
SMC 15 0.072 0.943 0.026
SMC 30 0.358 0.723 0.140
Metro 2 1.704 0.109 1.218
Metro 5 5.606 2.13e-05 2.966
Metro 8 4.418 0.00024 2.044
Metro 12 6.808 1.77e-06 3.621
Metro 15 7.441 8.89e-07 4.414
Metro 30 9.401 6.6e-09 4.448
DEMetro_Z 2 5.663 5.16e-05 4.378
DEMetro_Z 5 28.965 8.88e-12 166.697
DEMetro_Z 8 32.586 2.25e-12 138.406
DEMetro_Z 12 58.704 3.67e-15 303.788
DEMetro_Z 15 50.384 2.07e-14 307.443
DEMetro_Z 30 59.409 3.12e-15 282.855
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 7.447 1.28e-05 2.150
DEMetro_Z_vs_SMC 1 29.565 7.81e-12 8.535
DEMetro_Z_vs_SMC 2 32.556 2.74e-12 9.398
DEMetro_Z_vs_SMC 3 55.534 7.96e-15 16.031
DEMetro_Z_vs_SMC 4 50.416 2.3e-14 14.554
DEMetro_Z_vs_SMC 5 60.008 3.4e-15 17.323
HMC_vs_Metro 0 -2.041 0.066 -0.589
HMC_vs_Metro 1 -6.553 4.12e-05 -1.892
HMC_vs_Metro 2 -4.944 0.000439 -1.427
HMC_vs_Metro 3 -11.040 2.73e-07 -3.187
HMC_vs_Metro 4 -7.719 9.16e-06 -2.228
HMC_vs_Metro 5 -9.088 1.9e-06 -2.624
Metro_vs_DEMetro_Z 0 -4.372 0.00111 -1.262
Metro_vs_DEMetro_Z 1 -28.196 1.31e-11 -8.139
Metro_vs_DEMetro_Z 2 -30.995 4.68e-12 -8.947
Metro_vs_DEMetro_Z 3 -56.053 7.19e-15 -16.181
Metro_vs_DEMetro_Z 4 -49.632 2.73e-14 -14.328
Metro_vs_DEMetro_Z 5 -58.351 4.63e-15 -16.845
HMC_vs_SMC 0 1.192 0.258 0.344
HMC_vs_SMC 1 -1.744 0.109 -0.503
HMC_vs_SMC 2 2.136 0.056 0.617
HMC_vs_SMC 3 -1.367 0.199 -0.395
HMC_vs_SMC 4 0.309 0.763 0.089
HMC_vs_SMC 5 -1.067 0.309 -0.308
Metro_vs_SMC 0 2.538 0.0276 0.733
Metro_vs_SMC 1 4.678 0.000674 1.350
Metro_vs_SMC 2 6.734 3.23e-05 1.944
Metro_vs_SMC 3 7.855 7.77e-06 2.268
Metro_vs_SMC 4 8.813 2.57e-06 2.544
Metro_vs_SMC 5 13.150 4.52e-08 3.796
HMC_vs_DEMetro_Z 0 -7.811 8.2e-06 -2.255
HMC_vs_DEMetro_Z 1 -29.713 7.4e-12 -8.578
HMC_vs_DEMetro_Z 2 -32.990 2.37e-12 -9.524
HMC_vs_DEMetro_Z 3 -56.859 6.15e-15 -16.414
HMC_vs_DEMetro_Z 4 -49.535 2.79e-14 -14.300
HMC_vs_DEMetro_Z 5 -59.690 3.61e-15 -17.231
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.015 0.016 0.004 -0.264
HMC 5 0.014 0.014 0.003 -0.125
HMC 8 0.014 0.014 0.004 0.088
HMC 12 0.013 0.015 0.002 -0.961
HMC 15 0.014 0.014 0.002 0.123
HMC 30 0.013 0.014 0.002 -0.236
SMC 2 0.014 0.016 0.004 -0.609
SMC 5 0.015 0.014 0.003 0.422
SMC 8 0.013 0.014 0.004 -0.314
SMC 12 0.014 0.015 0.002 -0.392
SMC 15 0.014 0.014 0.002 0.026
SMC 30 0.014 0.014 0.002 0.140
Metro 2 0.020 0.016 0.004 1.218
Metro 5 0.024 0.014 0.003 2.966
Metro 8 0.023 0.014 0.004 2.044
Metro 12 0.022 0.015 0.002 3.621
Metro 15 0.022 0.014 0.002 4.414
Metro 30 0.023 0.014 0.002 4.448
DEMetro_Z 2 0.032 0.016 0.004 4.378
DEMetro_Z 5 0.567 0.014 0.003 166.697
DEMetro_Z 8 0.606 0.014 0.004 138.406
DEMetro_Z 12 0.579 0.015 0.002 303.788
DEMetro_Z 15 0.591 0.014 0.002 307.443
DEMetro_Z 30 0.573 0.014 0.002 282.855
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -0.665 0.513 -0.313
HMC 5 -0.745 0.464 -0.282
HMC 8 -0.177 0.861 -0.064
HMC 12 -1.892 0.0729 -0.912
HMC 15 -2.157 0.0426 -0.984
HMC 30 -2.223 0.0392 -0.750
SMC 2 -0.935 0.36 -0.424
SMC 5 -0.602 0.554 -0.285
SMC 8 0.537 0.597 0.188
SMC 12 -2.404 0.0252 -0.933
SMC 15 1.369 0.187 0.720
SMC 30 0.875 0.392 0.321
Metro 2 0.185 0.855 0.099
Metro 5 2.477 0.0231 1.345
Metro 8 4.605 0.00014 1.809
Metro 12 4.397 0.000379 2.594
Metro 15 7.107 1.55e-06 4.170
Metro 30 9.312 6.82e-09 4.318
DEMetro_Z 2 2.170 0.0479 1.823
DEMetro_Z 5 4.971 0.000422 201.361
DEMetro_Z 8 8.122 5.66e-06 598.100
DEMetro_Z 12 9.939 7.86e-07 2062.705
DEMetro_Z 15 9.800 9.04e-07 2485.359
DEMetro_Z 30 14.784 1.33e-08 2994.180
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -2.255 0.0455 -0.651
HMC_vs_DEMetro_Z 1 -4.976 0.000418 -1.436
HMC_vs_DEMetro_Z 2 -8.125 5.64e-06 -2.345
HMC_vs_DEMetro_Z 3 -9.938 7.87e-07 -2.869
HMC_vs_DEMetro_Z 4 -9.806 8.99e-07 -2.831
HMC_vs_DEMetro_Z 5 -14.792 1.32e-08 -4.270
Metro_vs_SMC 0 1.255 0.236 0.362
Metro_vs_SMC 1 3.119 0.00977 0.900
Metro_vs_SMC 2 5.908 0.000102 1.706
Metro_vs_SMC 3 6.796 2.97e-05 1.962
Metro_vs_SMC 4 5.715 0.000135 1.650
Metro_vs_SMC 5 8.287 4.67e-06 2.392
Metro_vs_DEMetro_Z 0 -1.827 0.0949 -0.527
Metro_vs_DEMetro_Z 1 -4.924 0.000454 -1.421
Metro_vs_DEMetro_Z 2 -8.103 5.78e-06 -2.339
Metro_vs_DEMetro_Z 3 -9.928 7.95e-07 -2.866
Metro_vs_DEMetro_Z 4 -9.783 9.2e-07 -2.824
Metro_vs_DEMetro_Z 5 -14.753 1.36e-08 -4.259
HMC_vs_Metro 0 -0.815 0.432 -0.235
HMC_vs_Metro 1 -4.472 0.000943 -1.291
HMC_vs_Metro 2 -5.958 9.48e-05 -1.720
HMC_vs_Metro 3 -8.758 2.73e-06 -2.528
HMC_vs_Metro 4 -8.257 4.83e-06 -2.384
HMC_vs_Metro 5 -11.513 1.78e-07 -3.323
HMC_vs_SMC 0 0.299 0.771 0.086
HMC_vs_SMC 1 0.008 0.994 0.002
HMC_vs_SMC 2 -1.233 0.243 -0.356
HMC_vs_SMC 3 0.048 0.962 0.014
HMC_vs_SMC 4 -4.647 0.000708 -1.342
HMC_vs_SMC 5 -5.660 0.000147 -1.634
DEMetro_Z_vs_SMC 0 2.228 0.0477 0.643
DEMetro_Z_vs_SMC 1 4.998 0.000404 1.443
DEMetro_Z_vs_SMC 2 8.121 5.66e-06 2.344
DEMetro_Z_vs_SMC 3 9.939 7.86e-07 2.869
DEMetro_Z_vs_SMC 4 9.805 9e-07 2.830
DEMetro_Z_vs_SMC 5 14.780 1.33e-08 4.267
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.023 0.025 0.008 -0.313
HMC 5 0.020 0.022 0.006 -0.282
HMC 8 0.021 0.021 0.009 -0.064
HMC 12 0.020 0.024 0.004 -0.912
HMC 15 0.019 0.022 0.004 -0.984
HMC 30 0.018 0.021 0.004 -0.750
SMC 2 0.022 0.025 0.008 -0.424
SMC 5 0.020 0.022 0.006 -0.285
SMC 8 0.023 0.021 0.009 0.188
SMC 12 0.020 0.024 0.004 -0.933
SMC 15 0.025 0.022 0.004 0.720
SMC 30 0.022 0.021 0.004 0.321
Metro 2 0.026 0.025 0.008 0.099
Metro 5 0.030 0.022 0.006 1.345
Metro 8 0.038 0.021 0.009 1.809
Metro 12 0.034 0.024 0.004 2.594
Metro 15 0.037 0.022 0.004 4.170
Metro 30 0.038 0.021 0.004 4.318
DEMetro_Z 2 0.040 0.025 0.008 1.823
DEMetro_Z 5 1.292 0.022 0.006 201.361
DEMetro_Z 8 5.540 0.021 0.009 598.100
DEMetro_Z 12 7.877 0.024 0.004 2062.705
DEMetro_Z 15 8.945 0.022 0.004 2485.359
DEMetro_Z 30 11.400 0.021 0.004 2994.180
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.070 0.0061 1.542
HMC 5 2.114 0.0478 1.103
HMC 8 2.265 0.0354 1.191
HMC 12 3.034 0.00851 2.267
HMC 15 2.057 0.0536 1.075
HMC 30 7.618 2.13e-07 3.654
SMC 2 -0.147 0.884 -0.062
SMC 5 -0.156 0.877 -0.069
SMC 8 -0.451 0.657 -0.177
SMC 12 0.232 0.819 0.113
SMC 15 -1.159 0.26 -0.563
SMC 30 0.302 0.766 0.112
Metro 2 0.930 0.365 0.556
Metro 5 6.382 2.8e-06 3.048
Metro 8 5.713 1.9e-05 3.137
Metro 12 10.039 1.56e-08 6.113
Metro 15 4.471 0.000386 2.931
Metro 30 9.179 8.31e-08 5.946
DEMetro_Z 2 1.767 0.0966 1.184
DEMetro_Z 5 3.271 0.00745 1486.494
DEMetro_Z 8 5.776 0.000123 3467.223
DEMetro_Z 12 5.507 0.000184 6057.266
DEMetro_Z 15 7.754 8.78e-06 4080.764
DEMetro_Z 30 16.805 3.43e-09 5266.334
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 2.607 0.0244 0.753
HMC_vs_SMC 1 2.125 0.0571 0.613
HMC_vs_SMC 2 2.590 0.0251 0.748
HMC_vs_SMC 3 3.145 0.00933 0.908
HMC_vs_SMC 4 3.880 0.00256 1.120
HMC_vs_SMC 5 8.384 4.17e-06 2.420
Metro_vs_DEMetro_Z 0 -0.869 0.403 -0.251
Metro_vs_DEMetro_Z 1 -3.265 0.00754 -0.942
Metro_vs_DEMetro_Z 2 -5.771 0.000124 -1.666
Metro_vs_DEMetro_Z 3 -5.501 0.000186 -1.588
Metro_vs_DEMetro_Z 4 -7.747 8.85e-06 -2.236
Metro_vs_DEMetro_Z 5 -16.788 3.46e-09 -4.846
HMC_vs_Metro 0 1.648 0.128 0.476
HMC_vs_Metro 1 -3.773 0.00308 -1.089
HMC_vs_Metro 2 -3.113 0.00987 -0.899
HMC_vs_Metro 3 -4.532 0.000854 -1.308
HMC_vs_Metro 4 -2.938 0.0135 -0.848
HMC_vs_Metro 5 -3.345 0.00654 -0.966
HMC_vs_DEMetro_Z 0 0.415 0.686 0.120
HMC_vs_DEMetro_Z 1 -3.268 0.00749 -0.943
HMC_vs_DEMetro_Z 2 -5.774 0.000124 -1.667
HMC_vs_DEMetro_Z 3 -5.504 0.000185 -1.589
HMC_vs_DEMetro_Z 4 -7.750 8.82e-06 -2.237
HMC_vs_DEMetro_Z 5 -16.793 3.45e-09 -4.848
Metro_vs_SMC 0 0.813 0.433 0.235
Metro_vs_SMC 1 11.361 2.04e-07 3.280
Metro_vs_SMC 2 7.972 6.75e-06 2.301
Metro_vs_SMC 3 11.902 1.27e-07 3.436
Metro_vs_SMC 4 5.648 0.000149 1.630
Metro_vs_SMC 5 11.004 2.82e-07 3.177
DEMetro_Z_vs_SMC 0 2.028 0.0675 0.585
DEMetro_Z_vs_SMC 1 3.272 0.00744 0.945
DEMetro_Z_vs_SMC 2 5.778 0.000123 1.668
DEMetro_Z_vs_SMC 3 5.507 0.000184 1.590
DEMetro_Z_vs_SMC 4 7.756 8.76e-06 2.239
DEMetro_Z_vs_SMC 5 16.801 3.44e-09 4.850
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.050 0.030 0.013 1.542
HMC 5 0.036 0.027 0.008 1.103
HMC 8 0.037 0.028 0.008 1.191
HMC 12 0.039 0.031 0.004 2.267
HMC 15 0.037 0.032 0.005 1.075
HMC 30 0.046 0.030 0.004 3.654
SMC 2 0.029 0.030 0.013 -0.062
SMC 5 0.027 0.027 0.008 -0.069
SMC 8 0.026 0.028 0.008 -0.177
SMC 12 0.031 0.031 0.004 0.113
SMC 15 0.029 0.032 0.005 -0.563
SMC 30 0.031 0.030 0.004 0.112
Metro 2 0.037 0.030 0.013 0.556
Metro 5 0.052 0.027 0.008 3.048
Metro 8 0.051 0.028 0.008 3.137
Metro 12 0.054 0.031 0.004 6.113
Metro 15 0.046 0.032 0.005 2.931
Metro 30 0.055 0.030 0.004 5.946
DEMetro_Z 2 0.046 0.030 0.013 1.184
DEMetro_Z 5 12.111 0.027 0.008 1486.494
DEMetro_Z 8 26.231 0.028 0.008 3467.223
DEMetro_Z 12 23.478 0.031 0.004 6057.266
DEMetro_Z 15 19.925 0.032 0.005 4080.764
DEMetro_Z 30 21.766 0.030 0.004 5266.334
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.295 0.772 0.167
HMC 5 0.111 0.912 0.043
HMC 8 -0.101 0.921 -0.039
HMC 12 0.066 0.948 0.028
HMC 15 -0.490 0.629 -0.177
HMC 30 0.483 0.635 0.166
SMC 2 -1.196 0.248 -0.704
SMC 5 -0.669 0.511 -0.329
SMC 8 -0.135 0.894 -0.050
SMC 12 -1.884 0.0732 -0.715
SMC 15 1.058 0.303 0.536
SMC 30 1.202 0.242 0.458
Metro 2 1.818 0.0864 1.064
Metro 5 3.904 0.00125 2.542
Metro 8 4.942 6.59e-05 2.225
Metro 12 5.445 4.37e-05 3.287
Metro 15 7.722 5.79e-07 4.643
Metro 30 10.662 6.86e-09 6.544
DEMetro_Z 2 4.858 0.000271 4.232
DEMetro_Z 5 5.038 0.000379 292.306
DEMetro_Z 8 9.111 1.86e-06 921.418
DEMetro_Z 12 11.081 2.63e-07 2730.990
DEMetro_Z 15 10.176 6.21e-07 3333.560
DEMetro_Z 30 14.804 1.31e-08 4929.553
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -3.061 0.0108 -0.884
Metro_vs_DEMetro_Z 1 -4.989 0.00041 -1.440
Metro_vs_DEMetro_Z 2 -9.094 1.89e-06 -2.625
Metro_vs_DEMetro_Z 3 -11.071 2.65e-07 -3.196
Metro_vs_DEMetro_Z 4 -10.161 6.3e-07 -2.933
Metro_vs_DEMetro_Z 5 -14.775 1.34e-08 -4.265
DEMetro_Z_vs_SMC 0 4.358 0.00114 1.258
DEMetro_Z_vs_SMC 1 5.064 0.000364 1.462
DEMetro_Z_vs_SMC 2 9.116 1.85e-06 2.632
DEMetro_Z_vs_SMC 3 11.080 2.63e-07 3.199
DEMetro_Z_vs_SMC 4 10.180 6.19e-07 2.939
DEMetro_Z_vs_SMC 5 14.799 1.31e-08 4.272
HMC_vs_DEMetro_Z 0 -3.690 0.00356 -1.065
HMC_vs_DEMetro_Z 1 -5.031 0.000383 -1.452
HMC_vs_DEMetro_Z 2 -9.115 1.85e-06 -2.631
HMC_vs_DEMetro_Z 3 -11.074 2.64e-07 -3.197
HMC_vs_DEMetro_Z 4 -10.178 6.2e-07 -2.938
HMC_vs_DEMetro_Z 5 -14.806 1.31e-08 -4.274
HMC_vs_Metro 0 -1.387 0.193 -0.400
HMC_vs_Metro 1 -5.055 0.000369 -1.459
HMC_vs_Metro 2 -5.286 0.000258 -1.526
HMC_vs_Metro 3 -6.475 4.58e-05 -1.869
HMC_vs_Metro 4 -8.307 4.56e-06 -2.398
HMC_vs_Metro 5 -10.400 4.99e-07 -3.002
HMC_vs_SMC 0 2.961 0.0129 0.855
HMC_vs_SMC 1 0.880 0.398 0.254
HMC_vs_SMC 2 0.039 0.97 0.011
HMC_vs_SMC 3 2.318 0.0407 0.669
HMC_vs_SMC 4 -1.934 0.0793 -0.558
HMC_vs_SMC 5 -1.118 0.287 -0.323
Metro_vs_SMC 0 3.061 0.0108 0.884
Metro_vs_SMC 1 5.261 0.000268 1.519
Metro_vs_SMC 2 6.336 5.55e-05 1.829
Metro_vs_SMC 3 7.399 1.36e-05 2.136
Metro_vs_SMC 4 6.327 5.62e-05 1.826
Metro_vs_SMC 5 9.379 1.4e-06 2.707
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.033 0.032 0.004 0.167
HMC 5 0.029 0.029 0.004 0.043
HMC 8 0.029 0.029 0.005 -0.039
HMC 12 0.030 0.030 0.003 0.028
HMC 15 0.028 0.029 0.002 -0.177
HMC 30 0.029 0.028 0.002 0.166
SMC 2 0.029 0.032 0.004 -0.704
SMC 5 0.027 0.029 0.004 -0.329
SMC 8 0.029 0.029 0.005 -0.050
SMC 12 0.028 0.030 0.003 -0.715
SMC 15 0.030 0.029 0.002 0.536
SMC 30 0.029 0.028 0.002 0.458
Metro 2 0.037 0.032 0.004 1.064
Metro 5 0.039 0.029 0.004 2.542
Metro 8 0.041 0.029 0.005 2.225
Metro 12 0.038 0.030 0.003 3.287
Metro 15 0.039 0.029 0.002 4.643
Metro 30 0.041 0.028 0.002 6.544
DEMetro_Z 2 0.050 0.032 0.004 4.232
DEMetro_Z 5 1.183 0.029 0.004 292.306
DEMetro_Z 8 4.942 0.029 0.005 921.418
DEMetro_Z 12 6.874 0.030 0.003 2730.990
DEMetro_Z 15 7.723 0.029 0.002 3333.560
DEMetro_Z 30 9.397 0.028 0.002 4929.553
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.515 0.612 0.212
HMC 5 0.436 0.667 0.157
HMC 8 0.059 0.953 0.022
HMC 12 -1.076 0.294 -0.492
HMC 15 -0.881 0.388 -0.374
HMC 30 -0.604 0.554 -0.199
SMC 2 -1.491 0.151 -0.678
SMC 5 -0.635 0.532 -0.279
SMC 8 0.342 0.736 0.124
SMC 12 -3.019 0.00663 -1.097
SMC 15 1.457 0.162 0.789
SMC 30 0.389 0.701 0.134
Metro 2 0.954 0.352 0.488
Metro 5 3.731 0.00135 1.881
Metro 8 4.877 7.2e-05 1.922
Metro 12 5.296 5.14e-05 3.026
Metro 15 7.790 3.49e-07 4.355
Metro 30 9.623 3.25e-09 4.329
DEMetro_Z 2 3.162 0.00674 2.483
DEMetro_Z 5 10.560 4.11e-07 63.751
DEMetro_Z 8 28.577 1.04e-11 176.731
DEMetro_Z 12 47.858 3.9e-14 476.435
DEMetro_Z 15 74.633 2.74e-16 466.440
DEMetro_Z 30 93.607 2.06e-17 454.497
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 3.297 0.00712 0.952
DEMetro_Z_vs_SMC 1 10.719 3.68e-07 3.094
DEMetro_Z_vs_SMC 2 28.745 1.06e-11 8.298
DEMetro_Z_vs_SMC 3 47.650 4.26e-14 13.755
DEMetro_Z_vs_SMC 4 77.175 2.15e-16 22.278
DEMetro_Z_vs_SMC 5 94.925 2.21e-17 27.402
HMC_vs_Metro 0 -0.601 0.56 -0.174
HMC_vs_Metro 1 -4.801 0.000553 -1.386
HMC_vs_Metro 2 -5.276 0.000262 -1.523
HMC_vs_Metro 3 -8.831 2.52e-06 -2.549
HMC_vs_Metro 4 -8.249 4.88e-06 -2.381
HMC_vs_Metro 5 -12.798 5.98e-08 -3.695
Metro_vs_DEMetro_Z 0 -2.098 0.0598 -0.606
Metro_vs_DEMetro_Z 1 -10.562 4.27e-07 -3.049
Metro_vs_DEMetro_Z 2 -28.323 1.25e-11 -8.176
Metro_vs_DEMetro_Z 3 -48.072 3.87e-14 -13.877
Metro_vs_DEMetro_Z 4 -74.310 3.26e-16 -21.452
Metro_vs_DEMetro_Z 5 -89.001 4.49e-17 -25.692
HMC_vs_SMC 0 4.266 0.00133 1.232
HMC_vs_SMC 1 1.495 0.163 0.432
HMC_vs_SMC 2 -0.441 0.668 -0.127
HMC_vs_SMC 3 1.642 0.129 0.474
HMC_vs_SMC 4 -3.655 0.00379 -1.055
HMC_vs_SMC 5 -1.598 0.138 -0.461
Metro_vs_SMC 0 2.616 0.024 0.755
Metro_vs_SMC 1 5.427 0.000208 1.567
Metro_vs_SMC 2 7.442 1.29e-05 2.148
Metro_vs_SMC 3 8.348 4.35e-06 2.410
Metro_vs_SMC 4 5.645 0.00015 1.630
Metro_vs_SMC 5 9.632 1.07e-06 2.781
HMC_vs_DEMetro_Z 0 -2.522 0.0284 -0.728
HMC_vs_DEMetro_Z 1 -10.584 4.18e-07 -3.055
HMC_vs_DEMetro_Z 2 -28.419 1.2e-11 -8.204
HMC_vs_DEMetro_Z 3 -47.366 4.55e-14 -13.673
HMC_vs_DEMetro_Z 4 -75.776 2.63e-16 -21.875
HMC_vs_DEMetro_Z 5 -92.681 2.88e-17 -26.755
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.017 0.016 0.004 0.212
HMC 5 0.014 0.014 0.003 0.157
HMC 8 0.014 0.014 0.004 0.022
HMC 12 0.014 0.015 0.002 -0.492
HMC 15 0.013 0.014 0.002 -0.374
HMC 30 0.013 0.014 0.002 -0.199
SMC 2 0.014 0.016 0.004 -0.678
SMC 5 0.013 0.014 0.003 -0.279
SMC 8 0.014 0.014 0.004 0.124
SMC 12 0.013 0.015 0.002 -1.097
SMC 15 0.016 0.014 0.002 0.789
SMC 30 0.014 0.014 0.002 0.134
Metro 2 0.018 0.016 0.004 0.488
Metro 5 0.020 0.014 0.003 1.881
Metro 8 0.022 0.014 0.004 1.922
Metro 12 0.021 0.015 0.002 3.026
Metro 15 0.022 0.014 0.002 4.355
Metro 30 0.022 0.014 0.002 4.329
DEMetro_Z 2 0.025 0.016 0.004 2.483
DEMetro_Z 5 0.226 0.014 0.003 63.751
DEMetro_Z 8 0.770 0.014 0.004 176.731
DEMetro_Z 12 0.899 0.015 0.002 476.435
DEMetro_Z 15 0.890 0.014 0.002 466.440
DEMetro_Z 30 0.912 0.014 0.002 454.497
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
2 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
12 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
30 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
12 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
30 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2
5
8
12
15
30
Chain
2
5
8
12
15
30

Varying_only_Tails (MvStudentT, nu, 12 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -0.268 0.792 -0.096
HMC 2.5 -0.402 0.692 -0.179
HMC 3.0 -0.329 0.746 -0.168
HMC 4.0 1.315 0.202 0.509
HMC 10.0 -1.650 0.115 -0.575
HMC 50.0 0.754 0.459 0.333
SMC 2.1 -0.887 0.387 -0.296
SMC 2.5 0.478 0.637 0.189
SMC 3.0 -1.204 0.242 -0.512
SMC 4.0 -0.211 0.834 -0.084
SMC 10.0 -2.276 0.0367 -0.737
SMC 50.0 -0.244 0.81 -0.084
Metro 2.1 1.791 0.0896 0.963
Metro 2.5 1.422 0.183 11.101
Metro 3.0 1.795 0.0982 2.709
Metro 4.0 3.474 0.00345 2.568
Metro 10.0 0.992 0.333 0.463
Metro 50.0 3.256 0.00554 2.521
DEMetro_Z 2.1 1.218 0.236 0.459
DEMetro_Z 2.5 2.980 0.0112 3.602
DEMetro_Z 3.0 2.664 0.0183 2.134
DEMetro_Z 4.0 3.129 0.00765 2.783
DEMetro_Z 10.0 1.510 0.146 0.554
DEMetro_Z 50.0 3.558 0.00236 2.098
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -1.793 0.1 -0.518
HMC_vs_DEMetro_Z 1 -2.879 0.015 -0.831
HMC_vs_DEMetro_Z 2 -2.536 0.0277 -0.732
HMC_vs_DEMetro_Z 3 -2.288 0.0429 -0.661
HMC_vs_DEMetro_Z 4 -3.804 0.00292 -1.098
HMC_vs_DEMetro_Z 5 -2.650 0.0226 -0.765
Metro_vs_SMC 0 2.807 0.0171 0.810
Metro_vs_SMC 1 1.389 0.192 0.401
Metro_vs_SMC 2 2.273 0.0441 0.656
Metro_vs_SMC 3 3.169 0.00893 0.915
Metro_vs_SMC 4 3.315 0.00689 0.957
Metro_vs_SMC 5 3.659 0.00376 1.056
Metro_vs_DEMetro_Z 0 1.000 0.339 0.289
Metro_vs_DEMetro_Z 1 0.915 0.38 0.264
Metro_vs_DEMetro_Z 2 0.307 0.765 0.088
Metro_vs_DEMetro_Z 3 -0.217 0.832 -0.063
Metro_vs_DEMetro_Z 4 -0.210 0.837 -0.061
Metro_vs_DEMetro_Z 5 0.474 0.645 0.137
HMC_vs_Metro 0 -2.447 0.0324 -0.706
HMC_vs_Metro 1 -1.427 0.181 -0.412
HMC_vs_Metro 2 -2.077 0.062 -0.600
HMC_vs_Metro 3 -3.249 0.00774 -0.938
HMC_vs_Metro 4 -2.419 0.0341 -0.698
HMC_vs_Metro 5 -2.421 0.034 -0.699
HMC_vs_SMC 0 1.259 0.234 0.363
HMC_vs_SMC 1 -0.772 0.456 -0.223
HMC_vs_SMC 2 0.975 0.35 0.282
HMC_vs_SMC 3 1.417 0.184 0.409
HMC_vs_SMC 4 0.720 0.487 0.208
HMC_vs_SMC 5 0.993 0.342 0.287
DEMetro_Z_vs_SMC 0 4.078 0.00183 1.177
DEMetro_Z_vs_SMC 1 3.165 0.00899 0.914
DEMetro_Z_vs_SMC 2 3.141 0.0094 0.907
DEMetro_Z_vs_SMC 3 3.227 0.00807 0.931
DEMetro_Z_vs_SMC 4 5.298 0.000253 1.529
DEMetro_Z_vs_SMC 5 4.233 0.00141 1.222
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.068 0.072 0.040 -0.096
HMC 2.5 0.037 0.040 0.019 -0.179
HMC 3.0 0.042 0.045 0.018 -0.168
HMC 4.0 0.031 0.025 0.013 0.509
HMC 10.0 0.019 0.029 0.016 -0.575
HMC 50.0 0.019 0.016 0.010 0.333
SMC 2.1 0.060 0.072 0.040 -0.296
SMC 2.5 0.044 0.040 0.019 0.189
SMC 3.0 0.036 0.045 0.018 -0.512
SMC 4.0 0.024 0.025 0.013 -0.084
SMC 10.0 0.017 0.029 0.016 -0.737
SMC 50.0 0.015 0.016 0.010 -0.084
Metro 2.1 0.110 0.072 0.040 0.963
Metro 2.5 0.252 0.040 0.019 11.101
Metro 3.0 0.093 0.045 0.018 2.709
Metro 4.0 0.057 0.025 0.013 2.568
Metro 10.0 0.036 0.029 0.016 0.463
Metro 50.0 0.041 0.016 0.010 2.521
DEMetro_Z 2.1 0.090 0.072 0.040 0.459
DEMetro_Z 2.5 0.109 0.040 0.019 3.602
DEMetro_Z 3.0 0.083 0.045 0.018 2.134
DEMetro_Z 4.0 0.059 0.025 0.013 2.783
DEMetro_Z 10.0 0.037 0.029 0.016 0.554
DEMetro_Z 50.0 0.036 0.016 0.010 2.098
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -0.012 0.991 -0.005
HMC 2.5 -1.040 0.314 -0.336
HMC 3.0 0.843 0.415 0.981
HMC 4.0 2.498 0.0241 1.702
HMC 10.0 1.695 0.106 0.881
HMC 50.0 1.507 0.146 0.664
SMC 2.1 0.096 0.924 0.037
SMC 2.5 0.333 0.745 0.334
SMC 3.0 0.249 0.806 0.098
SMC 4.0 1.430 0.169 0.737
SMC 10.0 1.999 0.0603 1.072
SMC 50.0 1.986 0.0608 0.970
Metro 2.1 -0.158 0.876 -0.062
Metro 2.5 0.994 0.341 7.978
Metro 3.0 0.957 0.354 0.739
Metro 4.0 3.096 0.00902 3.780
Metro 10.0 7.110 3.26e-06 5.022
Metro 50.0 2.491 0.0221 1.301
DEMetro_Z 2.1 0.042 0.967 0.016
DEMetro_Z 2.5 0.232 0.819 0.079
DEMetro_Z 3.0 0.341 0.737 0.128
DEMetro_Z 4.0 3.630 0.00245 2.614
DEMetro_Z 10.0 3.235 0.00586 2.571
DEMetro_Z 50.0 2.250 0.0391 1.509
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -0.372 0.717 -0.107
HMC_vs_SMC 1 -0.676 0.513 -0.195
HMC_vs_SMC 2 0.911 0.382 0.263
HMC_vs_SMC 3 1.575 0.144 0.455
HMC_vs_SMC 4 -0.251 0.806 -0.073
HMC_vs_SMC 5 -0.671 0.516 -0.194
Metro_vs_DEMetro_Z 0 -2.924 0.0138 -0.844
Metro_vs_DEMetro_Z 1 0.977 0.349 0.282
Metro_vs_DEMetro_Z 2 0.826 0.427 0.238
Metro_vs_DEMetro_Z 3 0.768 0.459 0.222
Metro_vs_DEMetro_Z 4 2.454 0.032 0.708
Metro_vs_DEMetro_Z 5 -0.353 0.731 -0.102
HMC_vs_Metro 0 0.821 0.429 0.237
HMC_vs_Metro 1 -1.032 0.324 -0.298
HMC_vs_Metro 2 0.555 0.59 0.160
HMC_vs_Metro 3 -1.677 0.122 -0.484
HMC_vs_Metro 4 -4.596 0.000769 -1.327
HMC_vs_Metro 5 -1.119 0.287 -0.323
HMC_vs_DEMetro_Z 0 -0.312 0.761 -0.090
HMC_vs_DEMetro_Z 1 -2.542 0.0274 -0.734
HMC_vs_DEMetro_Z 2 0.739 0.475 0.213
HMC_vs_DEMetro_Z 3 -0.940 0.368 -0.271
HMC_vs_DEMetro_Z 4 -1.997 0.0711 -0.577
HMC_vs_DEMetro_Z 5 -1.038 0.322 -0.300
Metro_vs_SMC 0 -1.286 0.225 -0.371
Metro_vs_SMC 1 0.935 0.37 0.270
Metro_vs_SMC 2 1.157 0.272 0.334
Metro_vs_SMC 3 2.487 0.0302 0.718
Metro_vs_SMC 4 5.556 0.000171 1.604
Metro_vs_SMC 5 0.669 0.517 0.193
DEMetro_Z_vs_SMC 0 -0.261 0.799 -0.075
DEMetro_Z_vs_SMC 1 -0.273 0.79 -0.079
DEMetro_Z_vs_SMC 2 0.136 0.894 0.039
DEMetro_Z_vs_SMC 3 3.442 0.0055 0.994
DEMetro_Z_vs_SMC 4 1.472 0.169 0.425
DEMetro_Z_vs_SMC 5 0.797 0.442 0.230
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 8.711 8.779 15.112 -0.005
HMC 2.5 1.088 1.437 1.038 -0.336
HMC 3.0 1.638 0.730 0.925 0.981
HMC 4.0 0.226 0.121 0.062 1.702
HMC 10.0 0.048 0.034 0.016 0.881
HMC 50.0 0.037 0.028 0.015 0.664
SMC 2.1 9.337 8.779 15.112 0.037
SMC 2.5 1.784 1.437 1.038 0.334
SMC 3.0 0.821 0.730 0.925 0.098
SMC 4.0 0.166 0.121 0.062 0.737
SMC 10.0 0.051 0.034 0.016 1.072
SMC 50.0 0.042 0.028 0.015 0.970
Metro 2.1 7.849 8.779 15.112 -0.062
Metro 2.5 9.719 1.437 1.038 7.978
Metro 3.0 1.414 0.730 0.925 0.739
Metro 4.0 0.354 0.121 0.062 3.780
Metro 10.0 0.113 0.034 0.016 5.022
Metro 50.0 0.047 0.028 0.015 1.301
DEMetro_Z 2.1 9.025 8.779 15.112 0.016
DEMetro_Z 2.5 1.519 1.437 1.038 0.079
DEMetro_Z 3.0 0.849 0.730 0.925 0.128
DEMetro_Z 4.0 0.282 0.121 0.062 2.614
DEMetro_Z 10.0 0.074 0.034 0.016 2.571
DEMetro_Z 50.0 0.050 0.028 0.015 1.509
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.219 0.241 0.841
HMC 2.5 0.515 0.612 0.223
HMC 3.0 1.791 0.0966 1.781
HMC 4.0 3.586 0.00247 2.347
HMC 10.0 -0.595 0.56 -0.190
HMC 50.0 0.675 0.508 0.360
SMC 2.1 0.025 0.981 0.011
SMC 2.5 -0.567 0.577 -0.297
SMC 3.0 -0.491 0.629 -0.210
SMC 4.0 0.281 0.782 0.131
SMC 10.0 -1.699 0.109 -0.547
SMC 50.0 -0.065 0.949 -0.028
Metro 2.1 4.598 0.000161 2.165
Metro 2.5 1.463 0.171 16.383
Metro 3.0 3.186 0.00823 6.221
Metro 4.0 6.526 2.59e-05 8.188
Metro 10.0 4.240 0.000367 1.960
Metro 50.0 3.886 0.00177 3.541
DEMetro_Z 2.1 6.371 7.05e-06 3.856
DEMetro_Z 2.5 4.626 0.000585 6.411
DEMetro_Z 3.0 9.080 7.45e-08 5.634
DEMetro_Z 4.0 8.220 1.69e-06 8.247
DEMetro_Z 10.0 5.033 5.51e-05 1.865
DEMetro_Z 50.0 6.294 7.02e-06 3.654
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -2.980 0.0125 -0.860
Metro_vs_DEMetro_Z 1 0.846 0.415 0.244
Metro_vs_DEMetro_Z 2 0.285 0.781 0.082
Metro_vs_DEMetro_Z 3 -0.033 0.974 -0.009
Metro_vs_DEMetro_Z 4 0.225 0.826 0.065
Metro_vs_DEMetro_Z 5 -0.119 0.907 -0.034
DEMetro_Z_vs_SMC 0 10.438 4.81e-07 3.013
DEMetro_Z_vs_SMC 1 5.444 0.000203 1.572
DEMetro_Z_vs_SMC 2 9.213 1.67e-06 2.659
DEMetro_Z_vs_SMC 3 7.804 8.26e-06 2.253
DEMetro_Z_vs_SMC 4 11.701 1.51e-07 3.378
DEMetro_Z_vs_SMC 5 5.797 0.00012 1.674
HMC_vs_DEMetro_Z 0 -3.960 0.00224 -1.143
HMC_vs_DEMetro_Z 1 -4.786 0.000566 -1.382
HMC_vs_DEMetro_Z 2 -3.454 0.00539 -0.997
HMC_vs_DEMetro_Z 3 -4.650 0.000705 -1.342
HMC_vs_DEMetro_Z 4 -8.802 2.6e-06 -2.541
HMC_vs_DEMetro_Z 5 -4.125 0.00169 -1.191
HMC_vs_Metro 0 -1.652 0.127 -0.477
HMC_vs_Metro 1 -1.428 0.181 -0.412
HMC_vs_Metro 2 -3.537 0.00466 -1.021
HMC_vs_Metro 3 -4.598 0.000768 -1.327
HMC_vs_Metro 4 -6.021 8.66e-05 -1.738
HMC_vs_Metro 5 -2.910 0.0142 -0.840
HMC_vs_SMC 0 1.065 0.31 0.307
HMC_vs_SMC 1 0.915 0.38 0.264
HMC_vs_SMC 2 2.391 0.0358 0.690
HMC_vs_SMC 3 2.938 0.0135 0.848
HMC_vs_SMC 4 2.633 0.0233 0.760
HMC_vs_SMC 5 0.755 0.466 0.218
Metro_vs_SMC 0 5.034 0.000381 1.453
Metro_vs_SMC 1 1.473 0.169 0.425
Metro_vs_SMC 2 3.500 0.00497 1.010
Metro_vs_SMC 3 6.435 4.84e-05 1.858
Metro_vs_SMC 4 7.153 1.86e-05 2.065
Metro_vs_SMC 5 3.952 0.00226 1.141
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.154 0.122 0.038 0.841
HMC 2.5 0.092 0.089 0.014 0.223
HMC 3.0 0.092 0.068 0.013 1.781
HMC 4.0 0.059 0.046 0.006 2.347
HMC 10.0 0.035 0.037 0.010 -0.190
HMC 50.0 0.030 0.028 0.006 0.360
SMC 2.1 0.123 0.122 0.038 0.011
SMC 2.5 0.085 0.089 0.014 -0.297
SMC 3.0 0.066 0.068 0.013 -0.210
SMC 4.0 0.046 0.046 0.006 0.131
SMC 10.0 0.031 0.037 0.010 -0.547
SMC 50.0 0.028 0.028 0.006 -0.028
Metro 2.1 0.204 0.122 0.038 2.165
Metro 2.5 0.316 0.089 0.014 16.383
Metro 3.0 0.150 0.068 0.013 6.221
Metro 4.0 0.093 0.046 0.006 8.188
Metro 10.0 0.056 0.037 0.010 1.960
Metro 50.0 0.049 0.028 0.006 3.541
DEMetro_Z 2.1 0.268 0.122 0.038 3.856
DEMetro_Z 2.5 0.178 0.089 0.014 6.411
DEMetro_Z 3.0 0.143 0.068 0.013 5.634
DEMetro_Z 4.0 0.093 0.046 0.006 8.247
DEMetro_Z 10.0 0.055 0.037 0.010 1.865
DEMetro_Z 50.0 0.050 0.028 0.006 3.654
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.321 0.206 0.902
HMC 2.5 0.169 0.869 0.051
HMC 3.0 1.940 0.0661 0.922
HMC 4.0 1.817 0.0834 0.829
HMC 10.0 -0.651 0.523 -0.217
HMC 50.0 0.024 0.981 0.011
SMC 2.1 0.045 0.965 0.019
SMC 2.5 -0.491 0.629 -0.176
SMC 3.0 -0.748 0.463 -0.370
SMC 4.0 -0.839 0.411 -0.350
SMC 10.0 -0.916 0.371 -0.312
SMC 50.0 -0.409 0.686 -0.173
Metro 2.1 5.762 2.52e-05 3.586
Metro 2.5 3.364 0.00561 4.574
Metro 3.0 7.202 1.52e-06 4.370
Metro 4.0 4.807 0.000244 3.616
Metro 10.0 3.877 0.000813 1.592
Metro 50.0 3.186 0.00644 2.513
DEMetro_Z 2.1 7.210 6.08e-06 6.764
DEMetro_Z 2.5 4.017 0.00166 5.133
DEMetro_Z 3.0 5.689 7.3e-05 5.594
DEMetro_Z 4.0 5.356 8.11e-05 3.908
DEMetro_Z 10.0 3.110 0.00514 1.213
DEMetro_Z 50.0 3.611 0.00193 1.961
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 7.283 1.58e-05 2.102
DEMetro_Z_vs_SMC 1 4.198 0.00149 1.212
DEMetro_Z_vs_SMC 2 6.435 4.84e-05 1.858
DEMetro_Z_vs_SMC 3 5.700 0.000138 1.645
DEMetro_Z_vs_SMC 4 6.044 8.38e-05 1.745
DEMetro_Z_vs_SMC 5 3.515 0.00484 1.015
HMC_vs_Metro 0 -3.445 0.00548 -0.994
HMC_vs_Metro 1 -3.260 0.0076 -0.941
HMC_vs_Metro 2 -4.556 0.000823 -1.315
HMC_vs_Metro 3 -4.244 0.00138 -1.225
HMC_vs_Metro 4 -5.021 0.00039 -1.449
HMC_vs_Metro 5 -2.859 0.0156 -0.825
Metro_vs_DEMetro_Z 0 -2.557 0.0267 -0.738
Metro_vs_DEMetro_Z 1 -0.255 0.803 -0.074
Metro_vs_DEMetro_Z 2 -1.086 0.301 -0.314
Metro_vs_DEMetro_Z 3 -0.257 0.802 -0.074
Metro_vs_DEMetro_Z 4 0.931 0.372 0.269
Metro_vs_DEMetro_Z 5 0.751 0.469 0.217
HMC_vs_SMC 0 1.150 0.275 0.332
HMC_vs_SMC 1 1.127 0.284 0.325
HMC_vs_SMC 2 2.842 0.016 0.820
HMC_vs_SMC 3 2.199 0.0501 0.635
HMC_vs_SMC 4 0.484 0.638 0.140
HMC_vs_SMC 5 0.499 0.628 0.144
Metro_vs_SMC 0 6.332 5.58e-05 1.828
Metro_vs_SMC 1 3.455 0.00538 0.997
Metro_vs_SMC 2 8.906 2.32e-06 2.571
Metro_vs_SMC 3 5.589 0.000163 1.613
Metro_vs_SMC 4 5.202 0.000294 1.502
Metro_vs_SMC 5 3.380 0.00615 0.976
HMC_vs_DEMetro_Z 0 -4.702 0.000648 -1.357
HMC_vs_DEMetro_Z 1 -4.182 0.00153 -1.207
HMC_vs_DEMetro_Z 2 -4.834 0.000524 -1.395
HMC_vs_DEMetro_Z 3 -3.654 0.00379 -1.055
HMC_vs_DEMetro_Z 4 -4.838 0.000521 -1.397
HMC_vs_DEMetro_Z 5 -2.644 0.0228 -0.763
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.018 0.014 0.004 0.902
HMC 2.5 0.015 0.015 0.004 0.051
HMC 3.0 0.019 0.015 0.004 0.922
HMC 4.0 0.017 0.014 0.004 0.829
HMC 10.0 0.013 0.015 0.006 -0.217
HMC 50.0 0.014 0.014 0.004 0.011
SMC 2.1 0.015 0.014 0.004 0.019
SMC 2.5 0.014 0.015 0.004 -0.176
SMC 3.0 0.014 0.015 0.004 -0.370
SMC 4.0 0.013 0.014 0.004 -0.350
SMC 10.0 0.013 0.015 0.006 -0.312
SMC 50.0 0.013 0.014 0.004 -0.173
Metro 2.1 0.030 0.014 0.004 3.586
Metro 2.5 0.035 0.015 0.004 4.574
Metro 3.0 0.033 0.015 0.004 4.370
Metro 4.0 0.027 0.014 0.004 3.616
Metro 10.0 0.024 0.015 0.006 1.592
Metro 50.0 0.024 0.014 0.004 2.513
DEMetro_Z 2.1 0.044 0.014 0.004 6.764
DEMetro_Z 2.5 0.038 0.015 0.004 5.133
DEMetro_Z 3.0 0.037 0.015 0.004 5.594
DEMetro_Z 4.0 0.028 0.014 0.004 3.908
DEMetro_Z 10.0 0.022 0.015 0.006 1.213
DEMetro_Z 50.0 0.022 0.014 0.004 1.961
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 0.505 0.619 0.223
HMC 2.5 0.276 0.785 0.122
HMC 3.0 0.266 0.793 0.097
HMC 4.0 1.027 0.317 0.536
HMC 10.0 -1.820 0.0843 -0.632
HMC 50.0 0.808 0.428 0.381
SMC 2.1 -0.920 0.368 -0.347
SMC 2.5 -0.044 0.965 -0.020
SMC 3.0 -0.849 0.405 -0.337
SMC 4.0 -0.012 0.99 -0.005
SMC 10.0 -1.524 0.143 -0.545
SMC 50.0 1.902 0.0705 0.735
Metro 2.1 1.524 0.145 0.872
Metro 2.5 3.885 0.002 4.350
Metro 3.0 2.269 0.0411 2.330
Metro 4.0 3.183 0.00678 2.738
Metro 10.0 1.379 0.182 0.614
Metro 50.0 3.133 0.00583 1.792
DEMetro_Z 2.1 3.064 0.00773 2.151
DEMetro_Z 2.5 3.358 0.00459 2.684
DEMetro_Z 3.0 2.854 0.0119 2.004
DEMetro_Z 4.0 4.355 0.00071 3.879
DEMetro_Z 10.0 1.592 0.127 0.808
DEMetro_Z 50.0 5.005 0.000138 3.390
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -2.908 0.0143 -0.839
HMC_vs_DEMetro_Z 1 -3.180 0.00876 -0.918
HMC_vs_DEMetro_Z 2 -2.655 0.0224 -0.766
HMC_vs_DEMetro_Z 3 -2.964 0.0129 -0.856
HMC_vs_DEMetro_Z 4 -3.798 0.00296 -1.096
HMC_vs_DEMetro_Z 5 -4.145 0.00163 -1.197
Metro_vs_SMC 0 2.251 0.0458 0.650
Metro_vs_SMC 1 4.261 0.00134 1.230
Metro_vs_SMC 2 2.520 0.0285 0.727
Metro_vs_SMC 3 2.970 0.0127 0.857
Metro_vs_SMC 4 3.801 0.00294 1.097
Metro_vs_SMC 5 2.419 0.0341 0.698
Metro_vs_DEMetro_Z 0 -1.652 0.127 -0.477
Metro_vs_DEMetro_Z 1 1.174 0.265 0.339
Metro_vs_DEMetro_Z 2 0.268 0.794 0.077
Metro_vs_DEMetro_Z 3 -1.062 0.311 -0.307
Metro_vs_DEMetro_Z 4 -0.507 0.622 -0.146
Metro_vs_DEMetro_Z 5 -1.941 0.0783 -0.560
HMC_vs_Metro 0 -1.058 0.313 -0.306
HMC_vs_Metro 1 -3.522 0.00478 -1.017
HMC_vs_Metro 2 -2.428 0.0335 -0.701
HMC_vs_Metro 3 -2.266 0.0446 -0.654
HMC_vs_Metro 4 -4.320 0.00121 -1.247
HMC_vs_Metro 5 -1.977 0.0736 -0.571
HMC_vs_SMC 0 1.494 0.163 0.431
HMC_vs_SMC 1 0.254 0.804 0.073
HMC_vs_SMC 2 1.174 0.265 0.339
HMC_vs_SMC 3 1.160 0.271 0.335
HMC_vs_SMC 4 -0.471 0.647 -0.136
HMC_vs_SMC 5 -0.758 0.464 -0.219
DEMetro_Z_vs_SMC 0 4.784 0.000568 1.381
DEMetro_Z_vs_SMC 1 3.339 0.00661 0.964
DEMetro_Z_vs_SMC 2 4.005 0.00207 1.156
DEMetro_Z_vs_SMC 3 4.274 0.00131 1.234
DEMetro_Z_vs_SMC 4 3.389 0.00605 0.978
DEMetro_Z_vs_SMC 5 4.036 0.00196 1.165
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.081 0.072 0.040 0.223
HMC 2.5 0.042 0.040 0.019 0.122
HMC 3.0 0.046 0.045 0.018 0.097
HMC 4.0 0.031 0.025 0.013 0.536
HMC 10.0 0.018 0.029 0.016 -0.632
HMC 50.0 0.020 0.016 0.010 0.381
SMC 2.1 0.058 0.072 0.040 -0.347
SMC 2.5 0.040 0.040 0.019 -0.020
SMC 3.0 0.039 0.045 0.018 -0.337
SMC 4.0 0.025 0.025 0.013 -0.005
SMC 10.0 0.020 0.029 0.016 -0.545
SMC 50.0 0.023 0.016 0.010 0.735
Metro 2.1 0.107 0.072 0.040 0.872
Metro 2.5 0.123 0.040 0.019 4.350
Metro 3.0 0.086 0.045 0.018 2.330
Metro 4.0 0.059 0.025 0.013 2.738
Metro 10.0 0.038 0.029 0.016 0.614
Metro 50.0 0.033 0.016 0.010 1.792
DEMetro_Z 2.1 0.158 0.072 0.040 2.151
DEMetro_Z 2.5 0.091 0.040 0.019 2.684
DEMetro_Z 3.0 0.080 0.045 0.018 2.004
DEMetro_Z 4.0 0.073 0.025 0.013 3.879
DEMetro_Z 10.0 0.041 0.029 0.016 0.808
DEMetro_Z 50.0 0.049 0.016 0.010 3.390
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 0.068 0.946 0.026
HMC 2.5 -0.872 0.393 -0.316
HMC 3.0 -0.695 0.495 -0.260
HMC 4.0 2.798 0.0115 1.481
HMC 10.0 1.285 0.218 0.917
HMC 50.0 1.409 0.173 0.573
SMC 2.1 0.035 0.973 0.014
SMC 2.5 -1.714 0.106 -0.548
SMC 3.0 -0.581 0.568 -0.208
SMC 4.0 1.471 0.161 0.989
SMC 10.0 2.896 0.00839 1.218
SMC 50.0 0.998 0.329 0.389
Metro 2.1 -0.103 0.919 -0.041
Metro 2.5 0.411 0.685 0.168
Metro 3.0 1.460 0.165 1.069
Metro 4.0 3.526 0.00285 2.355
Metro 10.0 1.984 0.07 2.396
Metro 50.0 2.082 0.053 1.281
DEMetro_Z 2.1 -0.164 0.871 -0.063
DEMetro_Z 2.5 -0.195 0.847 -0.072
DEMetro_Z 3.0 0.482 0.634 0.192
DEMetro_Z 4.0 4.106 0.00146 5.756
DEMetro_Z 10.0 3.661 0.00315 4.530
DEMetro_Z 50.0 4.222 0.000703 2.943
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.095 0.926 0.027
HMC_vs_SMC 1 0.793 0.444 0.229
HMC_vs_SMC 2 -0.848 0.414 -0.245
HMC_vs_SMC 3 0.618 0.549 0.179
HMC_vs_SMC 4 -0.437 0.671 -0.126
HMC_vs_SMC 5 0.421 0.682 0.121
Metro_vs_DEMetro_Z 0 0.748 0.47 0.216
Metro_vs_DEMetro_Z 1 0.731 0.48 0.211
Metro_vs_DEMetro_Z 2 1.208 0.252 0.349
Metro_vs_DEMetro_Z 3 -2.679 0.0215 -0.773
Metro_vs_DEMetro_Z 4 -2.071 0.0626 -0.598
Metro_vs_DEMetro_Z 5 -1.738 0.11 -0.502
HMC_vs_Metro 0 0.819 0.43 0.236
HMC_vs_Metro 1 -1.377 0.196 -0.398
HMC_vs_Metro 2 -1.899 0.0841 -0.548
HMC_vs_Metro 3 -1.286 0.225 -0.371
HMC_vs_Metro 4 -1.108 0.291 -0.320
HMC_vs_Metro 5 -1.271 0.23 -0.367
HMC_vs_DEMetro_Z 0 1.111 0.29 0.321
HMC_vs_DEMetro_Z 1 -0.682 0.509 -0.197
HMC_vs_DEMetro_Z 2 -3.299 0.00709 -0.952
HMC_vs_DEMetro_Z 3 -2.929 0.0137 -0.845
HMC_vs_DEMetro_Z 4 -2.428 0.0335 -0.701
HMC_vs_DEMetro_Z 5 -3.506 0.00491 -1.012
Metro_vs_SMC 0 -0.577 0.575 -0.167
Metro_vs_SMC 1 2.474 0.0309 0.714
Metro_vs_SMC 2 1.922 0.0809 0.555
Metro_vs_SMC 3 1.387 0.193 0.401
Metro_vs_SMC 4 1.042 0.32 0.301
Metro_vs_SMC 5 1.531 0.154 0.442
DEMetro_Z_vs_SMC 0 -0.784 0.45 -0.226
DEMetro_Z_vs_SMC 1 1.878 0.0871 0.542
DEMetro_Z_vs_SMC 2 2.949 0.0132 0.851
DEMetro_Z_vs_SMC 3 2.978 0.0126 0.860
DEMetro_Z_vs_SMC 4 3.042 0.0112 0.878
DEMetro_Z_vs_SMC 5 3.429 0.00564 0.990
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 9.175 8.779 15.112 0.026
HMC 2.5 1.108 1.437 1.038 -0.316
HMC 3.0 0.489 0.730 0.925 -0.260
HMC 4.0 0.212 0.121 0.062 1.481
HMC 10.0 0.048 0.034 0.016 0.917
HMC 50.0 0.036 0.028 0.015 0.573
SMC 2.1 8.984 8.779 15.112 0.014
SMC 2.5 0.868 1.437 1.038 -0.548
SMC 3.0 0.538 0.730 0.925 -0.208
SMC 4.0 0.182 0.121 0.062 0.989
SMC 10.0 0.053 0.034 0.016 1.218
SMC 50.0 0.033 0.028 0.015 0.389
Metro 2.1 8.166 8.779 15.112 -0.041
Metro 2.5 1.611 1.437 1.038 0.168
Metro 3.0 1.720 0.730 0.925 1.069
Metro 4.0 0.266 0.121 0.062 2.355
Metro 10.0 0.071 0.034 0.016 2.396
Metro 50.0 0.047 0.028 0.015 1.281
DEMetro_Z 2.1 7.831 8.779 15.112 -0.063
DEMetro_Z 2.5 1.361 1.437 1.038 -0.072
DEMetro_Z 3.0 0.908 0.730 0.925 0.192
DEMetro_Z 4.0 0.476 0.121 0.062 5.756
DEMetro_Z 10.0 0.105 0.034 0.016 4.530
DEMetro_Z 50.0 0.072 0.028 0.015 2.943
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.842 0.00966 1.274
HMC 2.5 1.488 0.151 0.662
HMC 3.0 1.704 0.105 0.584
HMC 4.0 3.225 0.00538 2.165
HMC 10.0 -0.991 0.337 -0.315
HMC 50.0 0.871 0.394 0.441
SMC 2.1 0.208 0.837 0.088
SMC 2.5 -0.521 0.608 -0.243
SMC 3.0 1.162 0.258 0.460
SMC 4.0 0.611 0.549 0.342
SMC 10.0 -0.607 0.551 -0.210
SMC 50.0 1.202 0.242 0.520
Metro 2.1 3.682 0.00187 2.244
Metro 2.5 4.274 0.00107 5.719
Metro 3.0 5.192 0.000178 5.288
Metro 4.0 5.901 5.82e-05 6.411
Metro 10.0 3.989 0.000778 2.082
Metro 50.0 4.508 0.000309 2.713
DEMetro_Z 2.1 4.561 0.000411 3.535
DEMetro_Z 2.5 6.691 8.98e-06 5.242
DEMetro_Z 3.0 8.801 3.98e-08 4.634
DEMetro_Z 4.0 8.670 1.68e-06 12.249
DEMetro_Z 10.0 5.894 9.74e-06 2.967
DEMetro_Z 50.0 6.869 7.52e-06 5.627
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -1.742 0.109 -0.503
Metro_vs_DEMetro_Z 1 0.285 0.781 0.082
Metro_vs_DEMetro_Z 2 0.603 0.559 0.174
Metro_vs_DEMetro_Z 3 -5.978 9.22e-05 -1.726
Metro_vs_DEMetro_Z 4 -1.718 0.114 -0.496
Metro_vs_DEMetro_Z 5 -3.256 0.00765 -0.940
DEMetro_Z_vs_SMC 0 5.589 0.000163 1.613
DEMetro_Z_vs_SMC 1 6.117 7.55e-05 1.766
DEMetro_Z_vs_SMC 2 7.587 1.08e-05 2.190
DEMetro_Z_vs_SMC 3 8.110 5.73e-06 2.341
DEMetro_Z_vs_SMC 4 8.736 2.8e-06 2.522
DEMetro_Z_vs_SMC 5 5.825 0.000115 1.681
HMC_vs_DEMetro_Z 0 -3.282 0.00731 -0.947
HMC_vs_DEMetro_Z 1 -5.629 0.000154 -1.625
HMC_vs_DEMetro_Z 2 -9.361 1.42e-06 -2.702
HMC_vs_DEMetro_Z 3 -6.150 7.21e-05 -1.775
HMC_vs_DEMetro_Z 4 -8.808 2.59e-06 -2.543
HMC_vs_DEMetro_Z 5 -5.624 0.000155 -1.623
HMC_vs_Metro 0 -1.513 0.159 -0.437
HMC_vs_Metro 1 -4.273 0.00131 -1.234
HMC_vs_Metro 2 -4.960 0.000429 -1.432
HMC_vs_Metro 3 -3.658 0.00377 -1.056
HMC_vs_Metro 4 -5.515 0.000182 -1.592
HMC_vs_Metro 5 -3.409 0.00584 -0.984
HMC_vs_SMC 0 3.246 0.00779 0.937
HMC_vs_SMC 1 1.920 0.0811 0.554
HMC_vs_SMC 2 0.367 0.721 0.106
HMC_vs_SMC 3 2.648 0.0226 0.765
HMC_vs_SMC 4 -0.507 0.622 -0.146
HMC_vs_SMC 5 -0.138 0.892 -0.040
Metro_vs_SMC 0 5.687 0.000141 1.642
Metro_vs_SMC 1 5.087 0.000351 1.468
Metro_vs_SMC 2 5.109 0.000339 1.475
Metro_vs_SMC 3 5.528 0.000179 1.596
Metro_vs_SMC 4 6.276 6.03e-05 1.812
Metro_vs_SMC 5 4.352 0.00115 1.256
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.170 0.122 0.038 1.274
HMC 2.5 0.098 0.089 0.014 0.662
HMC 3.0 0.076 0.068 0.013 0.584
HMC 4.0 0.058 0.046 0.006 2.165
HMC 10.0 0.034 0.037 0.010 -0.315
HMC 50.0 0.031 0.028 0.006 0.441
SMC 2.1 0.125 0.122 0.038 0.088
SMC 2.5 0.086 0.089 0.014 -0.243
SMC 3.0 0.075 0.068 0.013 0.460
SMC 4.0 0.048 0.046 0.006 0.342
SMC 10.0 0.035 0.037 0.010 -0.210
SMC 50.0 0.031 0.028 0.006 0.520
Metro 2.1 0.207 0.122 0.038 2.244
Metro 2.5 0.168 0.089 0.014 5.719
Metro 3.0 0.138 0.068 0.013 5.288
Metro 4.0 0.083 0.046 0.006 6.411
Metro 10.0 0.057 0.037 0.010 2.082
Metro 50.0 0.044 0.028 0.006 2.713
DEMetro_Z 2.1 0.255 0.122 0.038 3.535
DEMetro_Z 2.5 0.161 0.089 0.014 5.242
DEMetro_Z 3.0 0.130 0.068 0.013 4.634
DEMetro_Z 4.0 0.116 0.046 0.006 12.249
DEMetro_Z 10.0 0.066 0.037 0.010 2.967
DEMetro_Z 50.0 0.062 0.028 0.006 5.627
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.075 0.0537 1.285
HMC 2.5 1.456 0.16 0.609
HMC 3.0 1.867 0.0753 0.777
HMC 4.0 1.427 0.17 0.739
HMC 10.0 -0.283 0.781 -0.093
HMC 50.0 0.659 0.517 0.296
SMC 2.1 1.299 0.208 0.581
SMC 2.5 0.302 0.766 0.142
SMC 3.0 3.008 0.00661 1.343
SMC 4.0 -1.003 0.327 -0.394
SMC 10.0 -0.145 0.886 -0.049
SMC 50.0 0.412 0.684 0.162
Metro 2.1 4.244 0.000937 4.097
Metro 2.5 5.842 9.48e-06 2.809
Metro 3.0 3.643 0.0027 3.081
Metro 4.0 3.169 0.00623 2.222
Metro 10.0 4.174 0.000407 1.835
Metro 50.0 3.429 0.00313 2.017
DEMetro_Z 2.1 7.415 1.8e-06 5.119
DEMetro_Z 2.5 4.220 0.000433 2.127
DEMetro_Z 3.0 5.543 2.72e-05 3.043
DEMetro_Z 4.0 5.653 6.79e-05 5.055
DEMetro_Z 10.0 3.706 0.00128 1.671
DEMetro_Z 50.0 5.790 3.7e-05 4.271
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 7.289 1.57e-05 2.104
DEMetro_Z_vs_SMC 1 3.106 0.00999 0.897
DEMetro_Z_vs_SMC 2 2.382 0.0364 0.688
DEMetro_Z_vs_SMC 3 6.331 5.59e-05 1.828
DEMetro_Z_vs_SMC 4 4.905 0.000468 1.416
DEMetro_Z_vs_SMC 5 5.175 0.000306 1.494
HMC_vs_Metro 0 -2.659 0.0222 -0.768
HMC_vs_Metro 1 -5.172 0.000308 -1.493
HMC_vs_Metro 2 -2.783 0.0178 -0.803
HMC_vs_Metro 3 -2.348 0.0386 -0.678
HMC_vs_Metro 4 -5.383 0.000222 -1.554
HMC_vs_Metro 5 -2.714 0.0201 -0.784
Metro_vs_DEMetro_Z 0 -1.079 0.304 -0.311
Metro_vs_DEMetro_Z 1 1.171 0.266 0.338
Metro_vs_DEMetro_Z 2 0.049 0.962 0.014
Metro_vs_DEMetro_Z 3 -3.436 0.00556 -0.992
Metro_vs_DEMetro_Z 4 0.357 0.728 0.103
Metro_vs_DEMetro_Z 5 -2.762 0.0185 -0.797
HMC_vs_SMC 0 1.258 0.234 0.363
HMC_vs_SMC 1 0.891 0.392 0.257
HMC_vs_SMC 2 -1.187 0.26 -0.343
HMC_vs_SMC 3 2.900 0.0145 0.837
HMC_vs_SMC 4 -0.195 0.849 -0.056
HMC_vs_SMC 5 0.304 0.767 0.088
Metro_vs_SMC 0 4.073 0.00184 1.176
Metro_vs_SMC 1 4.345 0.00117 1.254
Metro_vs_SMC 2 1.993 0.0717 0.575
Metro_vs_SMC 3 4.647 0.000708 1.342
Metro_vs_SMC 4 6.462 4.66e-05 1.866
Metro_vs_SMC 5 3.999 0.00209 1.155
HMC_vs_DEMetro_Z 0 -4.438 0.000999 -1.281
HMC_vs_DEMetro_Z 1 -2.519 0.0285 -0.727
HMC_vs_DEMetro_Z 2 -4.661 0.000692 -1.346
HMC_vs_DEMetro_Z 3 -5.136 0.000325 -1.483
HMC_vs_DEMetro_Z 4 -5.694 0.000139 -1.644
HMC_vs_DEMetro_Z 5 -5.083 0.000353 -1.467
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.020 0.014 0.004 1.285
HMC 2.5 0.018 0.015 0.004 0.609
HMC 3.0 0.018 0.015 0.004 0.777
HMC 4.0 0.017 0.014 0.004 0.739
HMC 10.0 0.014 0.015 0.006 -0.093
HMC 50.0 0.015 0.014 0.004 0.296
SMC 2.1 0.017 0.014 0.004 0.581
SMC 2.5 0.016 0.015 0.004 0.142
SMC 3.0 0.021 0.015 0.004 1.343
SMC 4.0 0.013 0.014 0.004 -0.394
SMC 10.0 0.014 0.015 0.006 -0.049
SMC 50.0 0.014 0.014 0.004 0.162
Metro 2.1 0.032 0.014 0.004 4.097
Metro 2.5 0.028 0.015 0.004 2.809
Metro 3.0 0.027 0.015 0.004 3.081
Metro 4.0 0.022 0.014 0.004 2.222
Metro 10.0 0.026 0.015 0.006 1.835
Metro 50.0 0.022 0.014 0.004 2.017
DEMetro_Z 2.1 0.037 0.014 0.004 5.119
DEMetro_Z 2.5 0.025 0.015 0.004 2.127
DEMetro_Z 3.0 0.027 0.015 0.004 3.043
DEMetro_Z 4.0 0.032 0.014 0.004 5.055
DEMetro_Z 10.0 0.025 0.015 0.006 1.671
DEMetro_Z 50.0 0.032 0.014 0.004 4.271
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
2.1 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
2.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
50 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2.1 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
2.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
50 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2.1
2.5
3
4
10
50
Chain
2.1
2.5
3
4
10
50

Varying_only_Mode_distance (Mixture, mm, 12 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.412 0.000458 2.986
HMC 8 4.943 0.000433 26.334
HMC 10 4.192 0.0015 73.125
HMC 12 4.894 0.000469 26.636
HMC 15 3.935 0.00232 40.401
HMC 18 4.105 0.00172 18.745
SMC 5 -2.230 0.0403 -0.718
SMC 8 0.281 0.781 0.121
SMC 10 1.743 0.101 1.176
SMC 12 0.577 0.57 0.217
SMC 15 -0.121 0.905 -0.055
SMC 18 0.016 0.988 0.005
Metro 5 1.573 0.134 0.928
Metro 8 4.142 0.00158 12.886
Metro 10 3.886 0.00253 38.310
Metro 12 4.722 0.00062 30.101
Metro 15 4.841 0.000515 40.205
Metro 18 2.562 0.0263 12.699
DEMetro_Z 5 2.477 0.0223 1.217
DEMetro_Z 8 4.151 0.00148 8.426
DEMetro_Z 10 3.864 0.00263 49.270
DEMetro_Z 12 4.478 0.000919 22.146
DEMetro_Z 15 4.577 0.000791 45.000
DEMetro_Z 18 4.190 0.00146 13.559
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 3.191 0.00859 0.921
HMC_vs_DEMetro_Z 1 2.816 0.0168 0.813
HMC_vs_DEMetro_Z 2 1.545 0.151 0.446
HMC_vs_DEMetro_Z 3 0.731 0.48 0.211
HMC_vs_DEMetro_Z 4 -0.473 0.645 -0.137
HMC_vs_DEMetro_Z 5 1.161 0.27 0.335
Metro_vs_SMC 0 2.715 0.0201 0.784
Metro_vs_SMC 1 4.278 0.0013 1.235
Metro_vs_SMC 2 3.706 0.00347 1.070
Metro_vs_SMC 3 4.744 0.000606 1.369
Metro_vs_SMC 4 4.784 0.000568 1.381
Metro_vs_SMC 5 2.528 0.0281 0.730
Metro_vs_DEMetro_Z 0 -0.537 0.602 -0.155
Metro_vs_DEMetro_Z 1 1.854 0.0907 0.535
Metro_vs_DEMetro_Z 2 -0.575 0.577 -0.166
Metro_vs_DEMetro_Z 3 1.072 0.307 0.309
Metro_vs_DEMetro_Z 4 -0.490 0.634 -0.141
Metro_vs_DEMetro_Z 5 -0.204 0.842 -0.059
HMC_vs_Metro 0 2.900 0.0144 0.837
HMC_vs_Metro 1 2.122 0.0574 0.613
HMC_vs_Metro 2 1.611 0.136 0.465
HMC_vs_Metro 3 -0.593 0.565 -0.171
HMC_vs_Metro 4 0.032 0.975 0.009
HMC_vs_Metro 5 1.924 0.0806 0.555
HMC_vs_SMC 0 5.795 0.00012 1.673
HMC_vs_SMC 1 4.798 0.000555 1.385
HMC_vs_SMC 2 4.127 0.00168 1.191
HMC_vs_SMC 3 4.916 0.00046 1.419
HMC_vs_SMC 4 3.872 0.0026 1.118
HMC_vs_SMC 5 4.060 0.00188 1.172
DEMetro_Z_vs_SMC 0 4.139 0.00165 1.195
DEMetro_Z_vs_SMC 1 4.481 0.000929 1.294
DEMetro_Z_vs_SMC 2 3.744 0.00324 1.081
DEMetro_Z_vs_SMC 3 4.401 0.00106 1.271
DEMetro_Z_vs_SMC 4 4.483 0.000927 1.294
DEMetro_Z_vs_SMC 5 4.175 0.00155 1.205
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.137 0.049 0.030 2.986
HMC 8 1.175 0.063 0.042 26.334
HMC 10 1.808 0.042 0.024 73.125
HMC 12 1.772 0.075 0.064 26.636
HMC 15 2.242 0.099 0.053 40.401
HMC 18 2.456 0.111 0.125 18.745
SMC 5 0.027 0.049 0.030 -0.718
SMC 8 0.069 0.063 0.042 0.121
SMC 10 0.071 0.042 0.024 1.176
SMC 12 0.089 0.075 0.064 0.217
SMC 15 0.096 0.099 0.053 -0.055
SMC 18 0.112 0.111 0.125 0.005
Metro 5 0.076 0.049 0.030 0.928
Metro 8 0.607 0.063 0.042 12.886
Metro 10 0.967 0.042 0.024 38.310
Metro 12 1.993 0.075 0.064 30.101
Metro 15 2.231 0.099 0.053 40.205
Metro 18 1.699 0.111 0.125 12.699
DEMetro_Z 5 0.085 0.049 0.030 1.217
DEMetro_Z 8 0.419 0.063 0.042 8.426
DEMetro_Z 10 1.232 0.042 0.024 49.270
DEMetro_Z 12 1.486 0.075 0.064 22.146
DEMetro_Z 15 2.486 0.099 0.053 45.000
DEMetro_Z 18 1.807 0.111 0.125 13.559
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 0.196 0.847 0.070
HMC 8 3.513 0.00484 35.458
HMC 10 3.261 0.00758 130.694
HMC 12 3.294 0.00715 86.122
HMC 15 2.818 0.0167 83.299
HMC 18 2.907 0.0143 82.090
SMC 5 -0.133 0.896 -0.045
SMC 8 1.111 0.281 0.591
SMC 10 0.873 0.395 0.528
SMC 12 0.940 0.358 0.435
SMC 15 -1.718 0.1 -0.655
SMC 18 -0.511 0.614 -0.216
Metro 5 1.413 0.176 0.852
Metro 8 3.046 0.0109 9.389
Metro 10 2.365 0.0375 38.420
Metro 12 3.267 0.0075 111.721
Metro 15 3.300 0.00708 72.228
Metro 18 2.023 0.0681 60.816
DEMetro_Z 5 0.601 0.554 0.230
DEMetro_Z 8 2.792 0.0166 4.593
DEMetro_Z 10 2.408 0.0347 63.999
DEMetro_Z 12 3.153 0.00919 62.378
DEMetro_Z 15 3.237 0.00792 92.831
DEMetro_Z 18 3.714 0.00341 43.992
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.360 0.725 0.104
HMC_vs_SMC 1 3.515 0.00484 1.015
HMC_vs_SMC 2 3.222 0.00814 0.930
HMC_vs_SMC 3 3.293 0.00717 0.951
HMC_vs_SMC 4 2.848 0.0159 0.822
HMC_vs_SMC 5 2.909 0.0142 0.840
Metro_vs_DEMetro_Z 0 1.052 0.315 0.304
Metro_vs_DEMetro_Z 1 1.561 0.147 0.451
Metro_vs_DEMetro_Z 2 -0.743 0.473 -0.214
Metro_vs_DEMetro_Z 3 1.229 0.245 0.355
Metro_vs_DEMetro_Z 4 -0.607 0.556 -0.175
Metro_vs_DEMetro_Z 5 0.646 0.531 0.187
HMC_vs_Metro 0 -1.384 0.194 -0.399
HMC_vs_Metro 1 2.339 0.0393 0.675
HMC_vs_Metro 2 2.018 0.0687 0.583
HMC_vs_Metro 3 -0.701 0.498 -0.202
HMC_vs_Metro 4 0.560 0.587 0.162
HMC_vs_Metro 5 1.831 0.0943 0.529
HMC_vs_DEMetro_Z 0 -0.464 0.652 -0.134
HMC_vs_DEMetro_Z 1 2.855 0.0157 0.824
HMC_vs_DEMetro_Z 2 2.117 0.0579 0.611
HMC_vs_DEMetro_Z 3 0.790 0.446 0.228
HMC_vs_DEMetro_Z 4 -0.326 0.751 -0.094
HMC_vs_DEMetro_Z 5 1.463 0.172 0.422
Metro_vs_SMC 0 1.582 0.142 0.457
Metro_vs_SMC 1 2.756 0.0187 0.796
Metro_vs_SMC 2 2.383 0.0363 0.688
Metro_vs_SMC 3 3.249 0.00775 0.938
Metro_vs_SMC 4 3.348 0.00651 0.966
Metro_vs_SMC 5 2.027 0.0676 0.585
DEMetro_Z_vs_SMC 0 0.974 0.351 0.281
DEMetro_Z_vs_SMC 1 2.134 0.0562 0.616
DEMetro_Z_vs_SMC 2 2.366 0.0374 0.683
DEMetro_Z_vs_SMC 3 3.132 0.00955 0.904
DEMetro_Z_vs_SMC 4 3.254 0.00768 0.939
DEMetro_Z_vs_SMC 5 3.700 0.0035 1.068
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.070 0.066 0.058 0.070
HMC 8 2.808 0.094 0.077 35.458
HMC 10 7.441 0.089 0.056 130.694
HMC 12 6.419 0.111 0.073 86.122
HMC 15 11.637 0.245 0.137 83.299
HMC 18 13.138 0.204 0.158 82.090
SMC 5 0.063 0.066 0.058 -0.045
SMC 8 0.139 0.094 0.077 0.591
SMC 10 0.118 0.089 0.056 0.528
SMC 12 0.143 0.111 0.073 0.435
SMC 15 0.156 0.245 0.137 -0.655
SMC 18 0.170 0.204 0.158 -0.216
Metro 5 0.115 0.066 0.058 0.852
Metro 8 0.812 0.094 0.077 9.389
Metro 10 2.250 0.089 0.056 38.420
Metro 12 8.294 0.111 0.073 111.721
Metro 15 10.123 0.245 0.137 72.228
Metro 18 9.786 0.204 0.158 60.816
DEMetro_Z 5 0.079 0.066 0.058 0.230
DEMetro_Z 8 0.445 0.094 0.077 4.593
DEMetro_Z 10 3.689 0.089 0.056 63.999
DEMetro_Z 12 4.680 0.111 0.073 62.378
DEMetro_Z 15 12.941 0.245 0.137 92.831
DEMetro_Z 18 7.135 0.204 0.158 43.992
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.375 0.000661 3.759
HMC 8 4.696 0.000646 28.716
HMC 10 4.102 0.00175 92.662
HMC 12 4.917 0.000453 29.384
HMC 15 3.916 0.0024 45.277
HMC 18 3.984 0.00212 22.049
SMC 5 -2.577 0.0201 -0.834
SMC 8 0.380 0.708 0.145
SMC 10 2.314 0.0345 1.546
SMC 12 0.280 0.782 0.105
SMC 15 -0.525 0.605 -0.225
SMC 18 0.050 0.961 0.016
Metro 5 1.883 0.079 1.348
Metro 8 4.139 0.0016 13.863
Metro 10 3.756 0.00317 45.463
Metro 12 4.632 0.00072 33.675
Metro 15 4.960 0.000426 44.703
Metro 18 2.577 0.0256 14.127
DEMetro_Z 5 4.223 0.000475 2.264
DEMetro_Z 8 4.322 0.00111 8.986
DEMetro_Z 10 3.745 0.00323 61.268
DEMetro_Z 12 4.418 0.00102 25.482
DEMetro_Z 15 4.658 0.000694 49.158
DEMetro_Z 18 4.168 0.00153 15.685
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -1.267 0.231 -0.366
Metro_vs_DEMetro_Z 1 1.779 0.103 0.514
Metro_vs_DEMetro_Z 2 -0.656 0.525 -0.189
Metro_vs_DEMetro_Z 3 0.921 0.377 0.266
Metro_vs_DEMetro_Z 4 -0.434 0.673 -0.125
Metro_vs_DEMetro_Z 5 -0.311 0.762 -0.090
DEMetro_Z_vs_SMC 0 5.865 0.000108 1.693
DEMetro_Z_vs_SMC 1 4.532 0.000854 1.308
DEMetro_Z_vs_SMC 2 3.625 0.00399 1.046
DEMetro_Z_vs_SMC 3 4.369 0.00112 1.261
DEMetro_Z_vs_SMC 4 4.607 0.000756 1.330
DEMetro_Z_vs_SMC 5 4.161 0.00159 1.201
HMC_vs_DEMetro_Z 0 1.853 0.0908 0.535
HMC_vs_DEMetro_Z 1 2.746 0.019 0.793
HMC_vs_DEMetro_Z 2 1.569 0.145 0.453
HMC_vs_DEMetro_Z 3 0.535 0.604 0.154
HMC_vs_DEMetro_Z 4 -0.358 0.727 -0.103
HMC_vs_DEMetro_Z 5 1.107 0.292 0.320
HMC_vs_Metro 0 2.603 0.0246 0.751
HMC_vs_Metro 1 2.062 0.0636 0.595
HMC_vs_Metro 2 1.699 0.117 0.490
HMC_vs_Metro 3 -0.638 0.536 -0.184
HMC_vs_Metro 4 0.080 0.938 0.023
HMC_vs_Metro 5 2.111 0.0584 0.609
HMC_vs_SMC 0 5.345 0.000236 1.543
HMC_vs_SMC 1 4.618 0.000743 1.333
HMC_vs_SMC 2 4.047 0.00192 1.168
HMC_vs_SMC 3 4.965 0.000426 1.433
HMC_vs_SMC 4 3.889 0.00252 1.123
HMC_vs_SMC 5 3.943 0.0023 1.138
Metro_vs_SMC 0 2.877 0.0151 0.830
Metro_vs_SMC 1 4.243 0.00138 1.225
Metro_vs_SMC 2 3.596 0.0042 1.038
Metro_vs_SMC 3 4.662 0.000691 1.346
Metro_vs_SMC 4 4.934 0.000447 1.424
Metro_vs_SMC 5 2.541 0.0274 0.734
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.133 0.059 0.020 3.759
HMC 8 1.070 0.074 0.035 28.716
HMC 10 1.689 0.054 0.018 92.662
HMC 12 1.581 0.083 0.051 29.384
HMC 15 2.063 0.111 0.043 45.277
HMC 18 2.304 0.117 0.099 22.049
SMC 5 0.042 0.059 0.020 -0.834
SMC 8 0.079 0.074 0.035 0.145
SMC 10 0.081 0.054 0.018 1.546
SMC 12 0.088 0.083 0.051 0.105
SMC 15 0.101 0.111 0.043 -0.225
SMC 18 0.118 0.117 0.099 0.016
Metro 5 0.086 0.059 0.020 1.348
Metro 8 0.555 0.074 0.035 13.863
Metro 10 0.856 0.054 0.018 45.463
Metro 12 1.799 0.083 0.051 33.675
Metro 15 2.038 0.111 0.043 44.703
Metro 18 1.518 0.117 0.099 14.127
DEMetro_Z 5 0.104 0.059 0.020 2.264
DEMetro_Z 8 0.386 0.074 0.035 8.986
DEMetro_Z 10 1.135 0.054 0.018 61.268
DEMetro_Z 12 1.382 0.083 0.051 25.482
DEMetro_Z 15 2.230 0.111 0.043 49.158
DEMetro_Z 18 1.673 0.117 0.099 15.685
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.716 0.000359 4.185
HMC 8 4.870 0.000489 31.545
HMC 10 4.266 0.00133 81.453
HMC 12 5.060 0.000361 31.448
HMC 15 4.030 0.00198 54.169
HMC 18 4.059 0.00187 22.645
SMC 5 -2.286 0.0332 -0.817
SMC 8 0.581 0.567 0.243
SMC 10 1.829 0.0867 1.252
SMC 12 0.524 0.605 0.208
SMC 15 -0.054 0.957 -0.025
SMC 18 -0.091 0.929 -0.029
Metro 5 2.020 0.0612 1.413
Metro 8 3.970 0.00215 15.154
Metro 10 3.934 0.00233 43.625
Metro 12 4.952 0.00043 34.682
Metro 15 4.939 0.000441 54.482
Metro 18 2.607 0.0243 15.246
DEMetro_Z 5 3.521 0.00275 2.229
DEMetro_Z 8 4.070 0.00175 9.824
DEMetro_Z 10 3.986 0.00213 56.481
DEMetro_Z 12 4.526 0.000853 26.290
DEMetro_Z 15 4.880 0.000486 59.439
DEMetro_Z 18 4.251 0.00133 16.816
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 4.307 0.00124 1.243
DEMetro_Z_vs_SMC 1 4.174 0.00155 1.205
DEMetro_Z_vs_SMC 2 3.877 0.00258 1.119
DEMetro_Z_vs_SMC 3 4.463 0.000957 1.288
DEMetro_Z_vs_SMC 4 4.799 0.000554 1.385
DEMetro_Z_vs_SMC 5 4.269 0.00132 1.232
HMC_vs_Metro 0 3.045 0.0111 0.879
HMC_vs_Metro 1 2.134 0.0562 0.616
HMC_vs_Metro 2 1.593 0.14 0.460
HMC_vs_Metro 3 -0.501 0.626 -0.145
HMC_vs_Metro 4 -0.039 0.97 -0.011
HMC_vs_Metro 5 1.992 0.0717 0.575
Metro_vs_DEMetro_Z 0 -1.063 0.311 -0.307
Metro_vs_DEMetro_Z 1 1.765 0.105 0.510
Metro_vs_DEMetro_Z 2 -0.603 0.559 -0.174
Metro_vs_DEMetro_Z 3 1.023 0.328 0.295
Metro_vs_DEMetro_Z 4 -0.412 0.688 -0.119
Metro_vs_DEMetro_Z 5 -0.307 0.764 -0.089
HMC_vs_SMC 0 5.392 0.000219 1.557
HMC_vs_SMC 1 4.764 0.000586 1.375
HMC_vs_SMC 2 4.209 0.00146 1.215
HMC_vs_SMC 3 5.085 0.000352 1.468
HMC_vs_SMC 4 3.982 0.00215 1.149
HMC_vs_SMC 5 4.035 0.00196 1.165
Metro_vs_SMC 0 2.872 0.0152 0.829
Metro_vs_SMC 1 4.019 0.00202 1.160
Metro_vs_SMC 2 3.794 0.00297 1.095
Metro_vs_SMC 3 4.977 0.000417 1.437
Metro_vs_SMC 4 4.894 0.000476 1.413
Metro_vs_SMC 5 2.594 0.0249 0.749
HMC_vs_DEMetro_Z 0 2.263 0.0449 0.653
HMC_vs_DEMetro_Z 1 2.847 0.0159 0.822
HMC_vs_DEMetro_Z 2 1.482 0.166 0.428
HMC_vs_DEMetro_Z 3 0.718 0.488 0.207
HMC_vs_DEMetro_Z 4 -0.418 0.684 -0.121
HMC_vs_DEMetro_Z 5 1.055 0.314 0.304
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.041 0.016 0.006 4.185
HMC 8 0.255 0.014 0.008 31.545
HMC 10 0.318 0.008 0.004 81.453
HMC 12 0.268 0.011 0.008 31.448
HMC 15 0.273 0.011 0.005 54.169
HMC 18 0.248 0.011 0.010 22.645
SMC 5 0.011 0.016 0.006 -0.817
SMC 8 0.016 0.014 0.008 0.243
SMC 10 0.013 0.008 0.004 1.252
SMC 12 0.012 0.011 0.008 0.208
SMC 15 0.011 0.011 0.005 -0.025
SMC 18 0.011 0.011 0.010 -0.029
Metro 5 0.024 0.016 0.006 1.413
Metro 8 0.130 0.014 0.008 15.154
Metro 10 0.174 0.008 0.004 43.625
Metro 12 0.294 0.011 0.008 34.682
Metro 15 0.275 0.011 0.005 54.482
Metro 18 0.170 0.011 0.010 15.246
DEMetro_Z 5 0.029 0.016 0.006 2.229
DEMetro_Z 8 0.089 0.014 0.008 9.824
DEMetro_Z 10 0.223 0.008 0.004 56.481
DEMetro_Z 12 0.226 0.011 0.008 26.290
DEMetro_Z 15 0.299 0.011 0.005 59.439
DEMetro_Z 18 0.187 0.011 0.010 16.816
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.160 0.00102 3.649
HMC 8 4.025 0.00199 30.056
HMC 10 226.759 5.03e-30 144.252
HMC 12 165.418 2.1e-35 65.305
HMC 15 195.478 6.36e-34 98.100
HMC 18 116.183 6.72e-32 50.088
SMC 5 -1.834 0.0855 -0.588
SMC 8 -0.198 0.845 -0.066
SMC 10 0.872 0.395 0.476
SMC 12 -0.295 0.771 -0.106
SMC 15 1.138 0.269 0.590
SMC 18 1.147 0.264 0.442
Metro 5 2.702 0.0158 1.790
Metro 8 3.195 0.00831 8.605
Metro 10 4.613 0.000748 83.311
Metro 12 27.159 1.09e-11 62.270
Metro 15 192.652 2.13e-33 98.396
Metro 18 115.751 7.6e-32 49.996
DEMetro_Z 5 2.350 0.0306 1.349
DEMetro_Z 8 2.467 0.0311 11.636
DEMetro_Z 10 5.607 0.000158 98.720
DEMetro_Z 12 5.012 0.000393 44.369
DEMetro_Z 15 8.454 3.81e-06 84.169
DEMetro_Z 18 119.486 2.2e-32 49.968
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 2.381 0.0364 0.687
HMC_vs_DEMetro_Z 1 1.897 0.0844 0.548
HMC_vs_DEMetro_Z 2 2.574 0.0259 0.743
HMC_vs_DEMetro_Z 3 2.358 0.0379 0.681
HMC_vs_DEMetro_Z 4 1.424 0.182 0.411
HMC_vs_DEMetro_Z 5 0.325 0.752 0.094
Metro_vs_SMC 0 4.320 0.00121 1.247
Metro_vs_SMC 1 3.340 0.0066 0.964
Metro_vs_SMC 2 4.583 0.000786 1.323
Metro_vs_SMC 3 25.793 3.44e-11 7.446
Metro_vs_SMC 4 175.890 2.52e-20 50.775
Metro_vs_SMC 5 118.417 1.95e-18 34.184
Metro_vs_DEMetro_Z 0 0.556 0.59 0.160
Metro_vs_DEMetro_Z 1 -0.477 0.643 -0.138
Metro_vs_DEMetro_Z 2 -0.573 0.578 -0.165
Metro_vs_DEMetro_Z 3 2.209 0.0493 0.638
Metro_vs_DEMetro_Z 4 1.444 0.176 0.417
Metro_vs_DEMetro_Z 5 0.080 0.938 0.023
HMC_vs_Metro 0 2.475 0.0309 0.714
HMC_vs_Metro 1 2.571 0.026 0.742
HMC_vs_Metro 2 3.424 0.00569 0.988
HMC_vs_Metro 3 1.349 0.204 0.389
HMC_vs_Metro 4 -1.850 0.0914 -0.534
HMC_vs_Metro 5 0.752 0.468 0.217
HMC_vs_SMC 0 5.241 0.000276 1.513
HMC_vs_SMC 1 4.049 0.00192 1.169
HMC_vs_SMC 2 182.426 1.68e-20 52.662
HMC_vs_SMC 3 176.638 2.4e-20 50.991
HMC_vs_SMC 4 162.486 6.01e-20 46.906
HMC_vs_SMC 5 120.182 1.66e-18 34.694
DEMetro_Z_vs_SMC 0 4.310 0.00123 1.244
DEMetro_Z_vs_SMC 1 2.460 0.0317 0.710
DEMetro_Z_vs_SMC 2 5.530 0.000178 1.596
DEMetro_Z_vs_SMC 3 4.951 0.000435 1.429
DEMetro_Z_vs_SMC 4 8.377 4.21e-06 2.418
DEMetro_Z_vs_SMC 5 123.276 1.25e-18 35.587
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.157 0.049 0.030 3.649
HMC 8 1.332 0.063 0.042 30.056
HMC 10 3.525 0.042 0.024 144.252
HMC 12 4.236 0.075 0.064 65.305
HMC 15 5.302 0.099 0.053 98.100
HMC 18 6.376 0.111 0.125 50.088
SMC 5 0.031 0.049 0.030 -0.588
SMC 8 0.061 0.063 0.042 -0.066
SMC 10 0.054 0.042 0.024 0.476
SMC 12 0.069 0.075 0.064 -0.106
SMC 15 0.130 0.099 0.053 0.590
SMC 18 0.166 0.111 0.125 0.442
Metro 5 0.102 0.049 0.030 1.790
Metro 8 0.427 0.063 0.042 8.605
Metro 10 2.054 0.042 0.024 83.311
Metro 12 4.043 0.075 0.064 62.270
Metro 15 5.318 0.099 0.053 98.396
Metro 18 6.364 0.111 0.125 49.996
DEMetro_Z 5 0.089 0.049 0.030 1.349
DEMetro_Z 8 0.555 0.063 0.042 11.636
DEMetro_Z 10 2.426 0.042 0.024 98.720
DEMetro_Z 12 2.902 0.075 0.064 44.369
DEMetro_Z 15 4.563 0.099 0.053 84.169
DEMetro_Z 18 6.361 0.111 0.125 49.968
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 0.539 0.595 0.203
HMC 8 2.814 0.0168 53.023
HMC 10 540.545 1.54e-38 312.694
HMC 12 551.289 1.29e-36 346.369
HMC 15 659.625 4.87e-48 288.854
HMC 18 856.075 4.82e-51 361.964
SMC 5 -0.149 0.883 -0.061
SMC 8 -0.050 0.961 -0.021
SMC 10 0.839 0.413 0.509
SMC 12 0.716 0.482 0.369
SMC 15 -1.197 0.244 -0.451
SMC 18 -0.068 0.946 -0.032
Metro 5 2.112 0.0494 1.233
Metro 8 2.312 0.0406 5.872
Metro 10 3.769 0.0031 157.935
Metro 12 16.014 5.68e-09 319.954
Metro 15 696.699 3.06e-49 288.913
Metro 18 919.373 1.14e-51 361.917
DEMetro_Z 5 2.026 0.0572 1.073
DEMetro_Z 8 1.993 0.0715 14.295
DEMetro_Z 10 5.200 0.000295 195.095
DEMetro_Z 12 4.733 0.000616 231.670
DEMetro_Z 15 7.597 1.06e-05 241.747
DEMetro_Z 18 795.045 6.82e-49 362.003
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.909 0.383 0.262
HMC_vs_SMC 1 2.837 0.0162 0.819
HMC_vs_SMC 2 667.254 1.08e-26 192.620
HMC_vs_SMC 3 642.666 1.63e-26 185.522
HMC_vs_SMC 4 712.510 5.23e-27 205.684
HMC_vs_SMC 5 1143.449 2.88e-29 330.085
Metro_vs_DEMetro_Z 0 0.350 0.733 0.101
Metro_vs_DEMetro_Z 1 -1.006 0.336 -0.290
Metro_vs_DEMetro_Z 2 -0.598 0.562 -0.172
Metro_vs_DEMetro_Z 3 1.899 0.0841 0.548
Metro_vs_DEMetro_Z 4 1.486 0.165 0.429
Metro_vs_DEMetro_Z 5 -0.824 0.428 -0.238
HMC_vs_Metro 0 -1.873 0.0878 -0.541
HMC_vs_Metro 1 2.421 0.034 0.699
HMC_vs_Metro 2 3.718 0.00339 1.073
HMC_vs_Metro 3 1.342 0.207 0.387
HMC_vs_Metro 4 -0.612 0.553 -0.177
HMC_vs_Metro 5 0.684 0.508 0.197
HMC_vs_DEMetro_Z 0 -1.746 0.109 -0.504
HMC_vs_DEMetro_Z 1 1.766 0.105 0.510
HMC_vs_DEMetro_Z 2 3.125 0.00966 0.902
HMC_vs_DEMetro_Z 3 2.342 0.0391 0.676
HMC_vs_DEMetro_Z 4 1.484 0.166 0.428
HMC_vs_DEMetro_Z 5 -0.585 0.57 -0.169
Metro_vs_SMC 0 1.940 0.0785 0.560
Metro_vs_SMC 1 2.230 0.0475 0.644
Metro_vs_SMC 2 3.772 0.00309 1.089
Metro_vs_SMC 3 16.058 5.55e-09 4.635
Metro_vs_SMC 4 786.504 1.76e-27 227.044
Metro_vs_SMC 5 1287.879 7.77e-30 371.779
DEMetro_Z_vs_SMC 0 1.980 0.0732 0.572
DEMetro_Z_vs_SMC 1 1.970 0.0745 0.569
DEMetro_Z_vs_SMC 2 5.158 0.000314 1.489
DEMetro_Z_vs_SMC 3 4.738 0.000611 1.368
DEMetro_Z_vs_SMC 4 7.585 1.08e-05 2.190
DEMetro_Z_vs_SMC 5 1111.850 3.91e-29 320.963
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.077 0.066 0.058 0.203
HMC 8 4.152 0.094 0.077 53.023
HMC 10 17.680 0.089 0.056 312.694
HMC 12 25.480 0.111 0.073 346.369
HMC 15 39.748 0.245 0.137 288.854
HMC 18 57.234 0.204 0.158 361.964
SMC 5 0.062 0.066 0.058 -0.061
SMC 8 0.092 0.094 0.077 -0.021
SMC 10 0.117 0.089 0.056 0.509
SMC 12 0.138 0.111 0.073 0.369
SMC 15 0.183 0.245 0.137 -0.451
SMC 18 0.199 0.204 0.158 -0.032
Metro 5 0.138 0.066 0.058 1.233
Metro 8 0.543 0.094 0.077 5.872
Metro 10 8.974 0.089 0.056 157.935
Metro 12 23.546 0.111 0.073 319.954
Metro 15 39.756 0.245 0.137 288.913
Metro 18 57.227 0.204 0.158 361.917
DEMetro_Z 5 0.128 0.066 0.058 1.073
DEMetro_Z 8 1.188 0.094 0.077 14.295
DEMetro_Z 10 11.064 0.089 0.056 195.095
DEMetro_Z 12 17.079 0.111 0.073 231.670
DEMetro_Z 15 33.306 0.245 0.137 241.747
DEMetro_Z 18 57.241 0.204 0.158 362.003
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.229 0.00104 4.610
HMC 8 3.920 0.00238 32.317
HMC 10 42.245 1.28e-13 178.506
HMC 12 34.801 5.66e-13 71.024
HMC 15 36.608 4.88e-13 104.228
HMC 18 37.400 1.18e-13 56.388
SMC 5 -2.150 0.0481 -0.679
SMC 8 -0.296 0.77 -0.100
SMC 10 1.474 0.159 0.891
SMC 12 0.077 0.939 0.028
SMC 15 0.826 0.419 0.449
SMC 18 1.051 0.305 0.403
Metro 5 3.488 0.00336 2.592
Metro 8 3.328 0.00657 9.803
Metro 10 4.506 0.000892 105.693
Metro 12 26.195 1.84e-11 66.954
Metro 15 47.503 1.87e-14 103.819
Metro 18 55.523 9.2e-17 56.330
DEMetro_Z 5 4.187 0.000651 2.614
DEMetro_Z 8 2.669 0.0217 12.524
DEMetro_Z 10 5.577 0.000166 117.886
DEMetro_Z 12 5.042 0.000375 49.496
DEMetro_Z 15 8.377 4.17e-06 93.009
DEMetro_Z 18 49.948 8.82e-16 56.742
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -0.025 0.98 -0.007
Metro_vs_DEMetro_Z 1 -0.417 0.685 -0.120
Metro_vs_DEMetro_Z 2 -0.382 0.71 -0.110
Metro_vs_DEMetro_Z 3 1.968 0.0748 0.568
Metro_vs_DEMetro_Z 4 0.944 0.366 0.272
Metro_vs_DEMetro_Z 5 -0.261 0.799 -0.075
DEMetro_Z_vs_SMC 0 5.972 9.29e-05 1.724
DEMetro_Z_vs_SMC 1 2.658 0.0223 0.767
DEMetro_Z_vs_SMC 2 5.465 0.000196 1.577
DEMetro_Z_vs_SMC 3 4.972 0.000421 1.435
DEMetro_Z_vs_SMC 4 8.324 4.47e-06 2.403
DEMetro_Z_vs_SMC 5 46.967 4.99e-14 13.558
HMC_vs_DEMetro_Z 0 1.743 0.109 0.503
HMC_vs_DEMetro_Z 1 1.882 0.0865 0.543
HMC_vs_DEMetro_Z 2 2.733 0.0195 0.789
HMC_vs_DEMetro_Z 3 2.210 0.0492 0.638
HMC_vs_DEMetro_Z 4 1.072 0.307 0.309
HMC_vs_DEMetro_Z 5 -0.180 0.86 -0.052
HMC_vs_Metro 0 1.955 0.0765 0.564
HMC_vs_Metro 1 2.441 0.0328 0.705
HMC_vs_Metro 2 3.000 0.0121 0.866
HMC_vs_Metro 3 1.158 0.272 0.334
HMC_vs_Metro 4 0.101 0.921 0.029
HMC_vs_Metro 5 0.032 0.975 0.009
HMC_vs_SMC 0 5.139 0.000324 1.484
HMC_vs_SMC 1 3.961 0.00223 1.143
HMC_vs_SMC 2 40.843 2.3e-13 11.790
HMC_vs_SMC 3 35.557 1.05e-12 10.265
HMC_vs_SMC 4 33.910 1.76e-12 9.789
HMC_vs_SMC 5 39.509 3.31e-13 11.405
Metro_vs_SMC 0 4.899 0.000472 1.414
Metro_vs_SMC 1 3.446 0.00546 0.995
Metro_vs_SMC 2 4.472 0.000944 1.291
Metro_vs_SMC 3 24.697 5.5e-11 7.129
Metro_vs_SMC 4 50.559 2.23e-14 14.595
Metro_vs_SMC 5 52.817 1.38e-14 15.247
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.150 0.059 0.020 4.610
HMC 8 1.195 0.074 0.035 32.317
HMC 10 3.203 0.054 0.018 178.506
HMC 12 3.703 0.083 0.051 71.024
HMC 15 4.604 0.111 0.043 104.228
HMC 18 5.710 0.117 0.099 56.388
SMC 5 0.045 0.059 0.020 -0.679
SMC 8 0.070 0.074 0.035 -0.100
SMC 10 0.070 0.054 0.018 0.891
SMC 12 0.084 0.083 0.051 0.028
SMC 15 0.130 0.111 0.043 0.449
SMC 18 0.157 0.117 0.099 0.403
Metro 5 0.110 0.059 0.020 2.592
Metro 8 0.414 0.074 0.035 9.803
Metro 10 1.919 0.054 0.018 105.693
Metro 12 3.496 0.083 0.051 66.954
Metro 15 4.586 0.111 0.043 103.819
Metro 18 5.705 0.117 0.099 56.330
DEMetro_Z 5 0.111 0.059 0.020 2.614
DEMetro_Z 8 0.508 0.074 0.035 12.524
DEMetro_Z 10 2.134 0.054 0.018 117.886
DEMetro_Z 12 2.606 0.083 0.051 49.496
DEMetro_Z 15 4.120 0.111 0.043 93.009
DEMetro_Z 18 5.745 0.117 0.099 56.742
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.190 0.00119 5.149
HMC 8 4.026 0.00199 35.713
HMC 10 80.982 3.38e-17 159.269
HMC 12 119.856 7.25e-26 74.448
HMC 15 100.182 3.2e-19 124.666
HMC 18 105.160 4.34e-27 57.316
SMC 5 -2.067 0.0529 -0.706
SMC 8 -0.160 0.874 -0.055
SMC 10 1.378 0.185 0.765
SMC 12 0.060 0.953 0.021
SMC 15 1.404 0.179 0.893
SMC 18 1.249 0.225 0.480
Metro 5 3.534 0.00317 2.751
Metro 8 3.295 0.00698 10.204
Metro 10 4.688 0.000662 93.520
Metro 12 28.542 6.95e-12 71.702
Metro 15 130.830 8.44e-22 127.493
Metro 18 90.624 2.28e-23 58.307
DEMetro_Z 5 3.408 0.00384 2.425
DEMetro_Z 8 2.507 0.0291 14.750
DEMetro_Z 10 5.641 0.000151 109.951
DEMetro_Z 12 5.108 0.000338 51.048
DEMetro_Z 15 8.640 3.1e-06 105.803
DEMetro_Z 18 100.998 5.7e-26 57.632
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 4.816 0.000539 1.390
DEMetro_Z_vs_SMC 1 2.491 0.03 0.719
DEMetro_Z_vs_SMC 2 5.532 0.000178 1.597
DEMetro_Z_vs_SMC 3 5.050 0.000372 1.458
DEMetro_Z_vs_SMC 4 8.528 3.54e-06 2.462
DEMetro_Z_vs_SMC 5 104.653 7.58e-18 30.211
HMC_vs_Metro 0 2.087 0.0609 0.603
HMC_vs_Metro 1 2.603 0.0246 0.751
HMC_vs_Metro 2 3.543 0.00461 1.023
HMC_vs_Metro 3 1.209 0.252 0.349
HMC_vs_Metro 4 -2.183 0.0516 -0.630
HMC_vs_Metro 5 -1.655 0.126 -0.478
Metro_vs_DEMetro_Z 0 0.344 0.737 0.099
Metro_vs_DEMetro_Z 1 -0.589 0.568 -0.170
Metro_vs_DEMetro_Z 2 -0.562 0.585 -0.162
Metro_vs_DEMetro_Z 3 2.259 0.0451 0.652
Metro_vs_DEMetro_Z 4 1.790 0.101 0.517
Metro_vs_DEMetro_Z 5 0.724 0.484 0.209
HMC_vs_SMC 0 5.034 0.000382 1.453
HMC_vs_SMC 1 4.053 0.00191 1.170
HMC_vs_SMC 2 83.457 9.11e-17 24.092
HMC_vs_SMC 3 120.156 1.66e-18 34.686
HMC_vs_SMC 4 91.885 3.17e-17 26.525
HMC_vs_SMC 5 117.868 2.05e-18 34.026
Metro_vs_SMC 0 4.620 0.00074 1.334
Metro_vs_SMC 1 3.387 0.00606 0.978
Metro_vs_SMC 2 4.665 0.000688 1.347
Metro_vs_SMC 3 27.480 1.73e-11 7.933
Metro_vs_SMC 4 129.149 7.51e-19 37.282
Metro_vs_SMC 5 81.885 1.12e-16 23.638
HMC_vs_DEMetro_Z 0 2.152 0.0544 0.621
HMC_vs_DEMetro_Z 1 1.775 0.104 0.512
HMC_vs_DEMetro_Z 2 2.488 0.0302 0.718
HMC_vs_DEMetro_Z 3 2.323 0.0404 0.670
HMC_vs_DEMetro_Z 4 1.640 0.129 0.473
HMC_vs_DEMetro_Z 5 -0.425 0.679 -0.123
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.046 0.016 0.006 5.149
HMC 8 0.287 0.014 0.008 35.713
HMC 10 0.615 0.008 0.004 159.269
HMC 12 0.620 0.011 0.008 74.448
HMC 15 0.615 0.011 0.005 124.666
HMC 18 0.610 0.011 0.010 57.316
SMC 5 0.011 0.016 0.006 -0.706
SMC 8 0.014 0.014 0.008 -0.055
SMC 10 0.011 0.008 0.004 0.765
SMC 12 0.011 0.011 0.008 0.021
SMC 15 0.015 0.011 0.005 0.893
SMC 18 0.016 0.011 0.010 0.480
Metro 5 0.032 0.016 0.006 2.751
Metro 8 0.092 0.014 0.008 10.204
Metro 10 0.364 0.008 0.004 93.520
Metro 12 0.597 0.011 0.008 71.702
Metro 15 0.628 0.011 0.005 127.493
Metro 18 0.620 0.011 0.010 58.307
DEMetro_Z 5 0.030 0.016 0.006 2.425
DEMetro_Z 8 0.127 0.014 0.008 14.750
DEMetro_Z 10 0.427 0.008 0.004 109.951
DEMetro_Z 12 0.428 0.011 0.008 51.048
DEMetro_Z 15 0.523 0.011 0.005 105.803
DEMetro_Z 18 0.613 0.011 0.010 57.632
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
12 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
18 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
12 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
18 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
5
8
10
12
15
18
Chain
5
8
10
12
15
18

two_attr_corr

▼

Vary_Correlation_with_high_Dimension (MvNormal, correlation, 12 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -5.228 0.00012 -1.620
HMC 0.3 1.006 0.333 0.972
HMC 0.5 1.986 0.0694 2.235
HMC 0.9 2.926 0.012 3.060
HMC 0.99 4.199 0.00137 8.610
SMC 0.0 -0.559 0.582 -0.209
SMC 0.3 -0.744 0.465 -0.347
SMC 0.5 0.193 0.849 0.078
SMC 0.9 0.039 0.97 0.016
SMC 0.99 0.001 0.999 0.000
Metro 0.0 10.457 5.83e-10 4.479
Metro 0.3 4.216 0.00141 15.173
Metro 0.5 4.761 0.000558 13.806
Metro 0.9 3.332 0.00665 21.488
Metro 0.99 3.321 0.00681 62.140
DEMetro_Z 0.0 23.966 7.61e-11 1952.023
DEMetro_Z 0.3 20.692 3.71e-10 1893.763
DEMetro_Z 0.5 24.301 6.54e-11 1030.809
DEMetro_Z 0.9 31.303 4.14e-12 497.796
DEMetro_Z 0.99 29.479 8e-12 589.174
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -23.985 7.55e-11 -6.924
HMC_vs_DEMetro_Z 0.3 -20.748 3.6e-10 -5.990
HMC_vs_DEMetro_Z 0.5 -24.020 7.43e-11 -6.934
HMC_vs_DEMetro_Z 0.9 -30.915 4.81e-12 -8.924
HMC_vs_DEMetro_Z 0.99 -28.421 1.2e-11 -8.204
Metro_vs_SMC 0.0 13.130 4.59e-08 3.790
Metro_vs_SMC 0.3 4.312 0.00123 1.245
Metro_vs_SMC 0.5 4.948 0.000437 1.428
Metro_vs_SMC 0.9 3.394 0.00599 0.980
Metro_vs_SMC 0.99 3.329 0.00672 0.961
Metro_vs_DEMetro_Z 0.0 -23.903 7.83e-11 -6.900
Metro_vs_DEMetro_Z 0.3 -20.427 4.26e-10 -5.897
Metro_vs_DEMetro_Z 0.5 -24.230 6.77e-11 -6.995
Metro_vs_DEMetro_Z 0.9 -28.265 1.27e-11 -8.160
Metro_vs_DEMetro_Z 0.99 -20.714 3.67e-10 -5.980
HMC_vs_Metro 0.0 -20.971 3.21e-10 -6.054
HMC_vs_Metro 0.3 -4.470 0.000947 -1.290
HMC_vs_Metro 0.5 -3.714 0.00342 -1.072
HMC_vs_Metro 0.9 -2.956 0.0131 -0.853
HMC_vs_Metro 0.99 -2.806 0.0171 -0.810
HMC_vs_SMC 0.0 -5.690 0.00014 -1.642
HMC_vs_SMC 0.3 1.633 0.131 0.471
HMC_vs_SMC 0.5 2.069 0.0629 0.597
HMC_vs_SMC 0.9 2.722 0.0199 0.786
HMC_vs_SMC 0.99 4.306 0.00124 1.243
DEMetro_Z_vs_SMC 0.0 23.960 7.64e-11 6.917
DEMetro_Z_vs_SMC 0.3 20.738 3.62e-10 5.987
DEMetro_Z_vs_SMC 0.5 24.273 6.64e-11 7.007
DEMetro_Z_vs_SMC 0.9 31.201 4.35e-12 9.007
DEMetro_Z_vs_SMC 0.99 29.564 7.82e-12 8.535
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.018 0.023 0.003 -1.620
HMC 0.3 0.025 0.021 0.004 0.972
HMC 0.5 0.036 0.021 0.007 2.235
HMC 0.9 0.065 0.021 0.014 3.060
HMC 0.99 0.107 0.015 0.011 8.610
SMC 0.0 0.022 0.023 0.003 -0.209
SMC 0.3 0.020 0.021 0.004 -0.347
SMC 0.5 0.021 0.021 0.007 0.078
SMC 0.9 0.021 0.021 0.014 0.016
SMC 0.99 0.015 0.015 0.011 0.000
Metro 0.0 0.039 0.023 0.003 4.479
Metro 0.3 0.077 0.021 0.004 15.173
Metro 0.5 0.117 0.021 0.007 13.806
Metro 0.9 0.331 0.021 0.014 21.488
Metro 0.99 0.681 0.015 0.011 62.140
DEMetro_Z 0.0 6.786 0.023 0.003 1952.023
DEMetro_Z 0.3 7.006 0.021 0.004 1893.763
DEMetro_Z 0.5 7.224 0.021 0.007 1030.809
DEMetro_Z 0.9 7.210 0.021 0.014 497.796
DEMetro_Z 0.99 6.336 0.015 0.011 589.174
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 6.301 2.5e-06 2.679
HMC 0.3 2.379 0.0269 1.104
HMC 0.5 2.972 0.00705 1.254
HMC 0.9 3.443 0.00451 3.711
HMC 0.99 3.507 0.00484 14.737
SMC 0.0 2.679 0.0137 1.130
SMC 0.3 1.237 0.232 0.663
SMC 0.5 1.423 0.169 0.592
SMC 0.9 -1.521 0.146 -0.504
SMC 0.99 2.284 0.038 1.779
Metro 0.0 9.320 4.34e-09 3.733
Metro 0.3 8.289 9.18e-07 6.882
Metro 0.5 3.669 0.00341 6.774
Metro 0.9 5.017 0.00038 19.851
Metro 0.99 2.437 0.033 175.933
DEMetro_Z 0.0 21.266 2.76e-10 36419.860
DEMetro_Z 0.3 26.041 3.1e-11 40573.602
DEMetro_Z 0.5 25.735 3.52e-11 19423.903
DEMetro_Z 0.9 18.711 1.09e-09 9802.503
DEMetro_Z 0.99 21.720 2.2e-10 11664.493
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 2.928 0.0137 0.845
HMC_vs_SMC 0.3 0.801 0.44 0.231
HMC_vs_SMC 0.5 1.751 0.108 0.505
HMC_vs_SMC 0.9 3.829 0.0028 1.105
HMC_vs_SMC 0.99 2.888 0.0148 0.834
Metro_vs_DEMetro_Z 0.0 -21.263 2.77e-10 -6.138
Metro_vs_DEMetro_Z 0.3 -26.031 3.11e-11 -7.515
Metro_vs_DEMetro_Z 0.5 -25.720 3.55e-11 -7.425
Metro_vs_DEMetro_Z 0.9 -18.636 1.14e-09 -5.380
Metro_vs_DEMetro_Z 0.99 -21.559 2.39e-10 -6.223
HMC_vs_Metro 0.0 -2.019 0.0686 -0.583
HMC_vs_Metro 0.3 -6.396 5.11e-05 -1.846
HMC_vs_Metro 0.5 -3.059 0.0109 -0.883
HMC_vs_Metro 0.9 -3.722 0.00337 -1.075
HMC_vs_Metro 0.99 -2.276 0.0438 -0.657
HMC_vs_DEMetro_Z 0.0 -21.265 2.77e-10 -6.139
HMC_vs_DEMetro_Z 0.3 -26.038 3.1e-11 -7.517
HMC_vs_DEMetro_Z 0.5 -25.736 3.52e-11 -7.429
HMC_vs_DEMetro_Z 0.9 -18.711 1.09e-09 -5.401
HMC_vs_DEMetro_Z 0.99 -21.679 2.25e-10 -6.258
Metro_vs_SMC 0.0 6.009 8.81e-05 1.735
Metro_vs_SMC 0.3 6.888 2.63e-05 1.988
Metro_vs_SMC 0.5 3.753 0.00319 1.083
Metro_vs_SMC 0.9 5.260 0.000269 1.518
Metro_vs_SMC 0.99 2.402 0.0351 0.693
DEMetro_Z_vs_SMC 0.0 21.265 2.77e-10 6.139
DEMetro_Z_vs_SMC 0.3 26.038 3.1e-11 7.516
DEMetro_Z_vs_SMC 0.5 25.738 3.52e-11 7.430
DEMetro_Z_vs_SMC 0.9 18.711 1.09e-09 5.401
DEMetro_Z_vs_SMC 0.99 21.721 2.2e-10 6.270
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.045 0.033 0.005 2.679
HMC 0.3 0.036 0.031 0.004 1.104
HMC 0.5 0.044 0.032 0.010 1.254
HMC 0.9 0.097 0.031 0.018 3.711
HMC 0.99 0.204 0.021 0.012 14.737
SMC 0.0 0.038 0.033 0.005 1.130
SMC 0.3 0.034 0.031 0.004 0.663
SMC 0.5 0.038 0.032 0.010 0.592
SMC 0.9 0.022 0.031 0.018 -0.504
SMC 0.99 0.043 0.021 0.012 1.779
Metro 0.0 0.050 0.033 0.005 3.733
Metro 0.3 0.061 0.031 0.004 6.882
Metro 0.5 0.099 0.032 0.010 6.774
Metro 0.9 0.381 0.031 0.018 19.851
Metro 0.99 2.205 0.021 0.012 175.933
DEMetro_Z 0.0 165.856 0.033 0.005 36419.860
DEMetro_Z 0.3 179.445 0.031 0.004 40573.602
DEMetro_Z 0.5 191.966 0.032 0.010 19423.903
DEMetro_Z 0.9 172.546 0.031 0.018 9802.503
DEMetro_Z 0.99 144.847 0.021 0.012 11664.493
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -1.765 0.0959 -0.575
HMC 0.3 1.901 0.0808 2.250
HMC 0.5 2.321 0.039 3.468
HMC 0.9 5.224 0.00014 4.580
HMC 0.99 6.074 6.96e-05 13.519
SMC 0.0 0.098 0.922 0.038
SMC 0.3 0.373 0.714 0.194
SMC 0.5 0.752 0.46 0.329
SMC 0.9 -0.307 0.762 -0.117
SMC 0.99 0.922 0.367 0.382
Metro 0.0 12.421 6.99e-11 6.101
Metro 0.3 4.683 0.000658 25.018
Metro 0.5 4.992 0.000397 21.603
Metro 0.9 4.645 0.000704 32.170
Metro 0.99 4.365 0.00113 113.701
DEMetro_Z 0.0 64.225 1.61e-15 5131.237
DEMetro_Z 0.3 49.829 2.61e-14 6147.386
DEMetro_Z 0.5 55.515 7.98e-15 3054.682
DEMetro_Z 0.9 53.448 1.2e-14 1091.043
DEMetro_Z 0.99 52.128 1.58e-14 1302.226
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -64.061 1.66e-15 -18.493
Metro_vs_DEMetro_Z 0.3 -49.880 2.58e-14 -14.399
Metro_vs_DEMetro_Z 0.5 -52.997 1.33e-14 -15.299
Metro_vs_DEMetro_Z 0.9 -46.393 5.71e-14 -13.392
Metro_vs_DEMetro_Z 0.99 -34.504 1.45e-12 -9.960
DEMetro_Z_vs_SMC 0.0 64.259 1.61e-15 18.550
DEMetro_Z_vs_SMC 0.3 49.875 2.59e-14 14.398
DEMetro_Z_vs_SMC 0.5 55.529 7.97e-15 16.030
DEMetro_Z_vs_SMC 0.9 53.472 1.21e-14 15.436
DEMetro_Z_vs_SMC 0.99 52.202 1.57e-14 15.070
HMC_vs_DEMetro_Z 0.0 -64.243 1.61e-15 -18.545
HMC_vs_DEMetro_Z 0.3 -49.882 2.58e-14 -14.400
HMC_vs_DEMetro_Z 0.5 -55.592 7.87e-15 -16.048
HMC_vs_DEMetro_Z 0.9 -52.366 1.52e-14 -15.117
HMC_vs_DEMetro_Z 0.99 -51.051 2e-14 -14.737
HMC_vs_Metro 0.0 -18.314 1.37e-09 -5.287
HMC_vs_Metro 0.3 -4.673 0.00068 -1.349
HMC_vs_Metro 0.5 -3.916 0.00241 -1.130
HMC_vs_Metro 0.9 -4.063 0.00187 -1.173
HMC_vs_Metro 0.99 -3.920 0.00239 -1.132
HMC_vs_SMC 0.0 -2.232 0.0474 -0.644
HMC_vs_SMC 0.3 1.907 0.0829 0.551
HMC_vs_SMC 0.5 2.234 0.0472 0.645
HMC_vs_SMC 0.9 5.350 0.000234 1.544
HMC_vs_SMC 0.99 5.889 0.000105 1.700
Metro_vs_SMC 0.0 14.097 2.19e-08 4.070
Metro_vs_SMC 0.3 4.551 0.000828 1.314
Metro_vs_SMC 0.5 5.060 0.000367 1.461
Metro_vs_SMC 0.9 4.748 0.000602 1.371
Metro_vs_SMC 0.99 4.336 0.00118 1.252
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.028 0.029 0.002 -0.575
HMC 0.3 0.031 0.028 0.002 2.250
HMC 0.5 0.039 0.027 0.004 3.468
HMC 0.9 0.072 0.027 0.010 4.580
HMC 0.99 0.120 0.021 0.007 13.519
SMC 0.0 0.029 0.029 0.002 0.038
SMC 0.3 0.028 0.028 0.002 0.194
SMC 0.5 0.028 0.027 0.004 0.329
SMC 0.9 0.026 0.027 0.010 -0.117
SMC 0.99 0.024 0.021 0.007 0.382
Metro 0.0 0.041 0.029 0.002 6.101
Metro 0.3 0.070 0.028 0.002 25.018
Metro 0.5 0.106 0.027 0.004 21.603
Metro 0.9 0.342 0.027 0.010 32.170
Metro 0.99 0.851 0.021 0.007 113.701
DEMetro_Z 0.0 10.138 0.029 0.002 5131.237
DEMetro_Z 0.3 10.538 0.028 0.002 6147.386
DEMetro_Z 0.5 11.226 0.027 0.004 3054.682
DEMetro_Z 0.9 10.723 0.027 0.010 1091.043
DEMetro_Z 0.99 9.530 0.021 0.007 1302.226
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -3.554 0.00248 -1.163
HMC 0.3 1.483 0.163 1.650
HMC 0.5 2.303 0.0384 2.299
HMC 0.9 5.594 5.76e-05 4.294
HMC 0.99 5.344 0.000206 10.975
SMC 0.0 -0.583 0.566 -0.241
SMC 0.3 -0.676 0.507 -0.339
SMC 0.5 0.683 0.502 0.276
SMC 0.9 -0.183 0.857 -0.073
SMC 0.99 1.171 0.255 0.445
Metro 0.0 9.553 2.53e-08 5.621
Metro 0.3 4.688 0.000648 20.933
Metro 0.5 5.265 0.00025 15.608
Metro 0.9 6.820 2.76e-05 30.523
Metro 0.99 6.953 2.39e-05 60.370
DEMetro_Z 0.0 57.856 4.56e-15 371.137
DEMetro_Z 0.3 54.863 8.45e-15 419.725
DEMetro_Z 0.5 41.859 1.4e-13 170.303
DEMetro_Z 0.9 94.669 8.48e-21 80.900
DEMetro_Z 0.99 55.494 1.82e-15 95.908
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 57.608 5.33e-15 16.630
DEMetro_Z_vs_SMC 0.3 56.149 7.06e-15 16.209
DEMetro_Z_vs_SMC 0.5 42.356 1.55e-13 12.227
DEMetro_Z_vs_SMC 0.9 93.273 2.68e-17 26.926
DEMetro_Z_vs_SMC 0.99 58.645 4.38e-15 16.929
HMC_vs_Metro 0.0 -13.651 3.06e-08 -3.941
HMC_vs_Metro 0.3 -4.907 0.000467 -1.416
HMC_vs_Metro 0.5 -4.221 0.00143 -1.219
HMC_vs_Metro 0.9 -6.012 8.77e-05 -1.736
HMC_vs_Metro 0.99 -5.616 0.000157 -1.621
Metro_vs_DEMetro_Z 0.0 -57.570 5.37e-15 -16.619
Metro_vs_DEMetro_Z 0.3 -42.624 1.44e-13 -12.304
Metro_vs_DEMetro_Z 0.5 -37.113 6.56e-13 -10.714
Metro_vs_DEMetro_Z 0.9 -11.941 1.22e-07 -3.447
Metro_vs_DEMetro_Z 0.99 -4.205 0.00147 -1.214
HMC_vs_SMC 0.0 -2.668 0.0219 -0.770
HMC_vs_SMC 0.3 1.966 0.075 0.568
HMC_vs_SMC 0.5 2.157 0.054 0.623
HMC_vs_SMC 0.9 6.123 7.49e-05 1.767
HMC_vs_SMC 0.99 5.122 0.000332 1.479
Metro_vs_SMC 0.0 10.139 6.44e-07 2.927
Metro_vs_SMC 0.3 4.662 0.000692 1.346
Metro_vs_SMC 0.5 5.269 0.000265 1.521
Metro_vs_SMC 0.9 7.010 2.24e-05 2.023
Metro_vs_SMC 0.99 6.843 2.79e-05 1.976
HMC_vs_DEMetro_Z 0.0 -58.133 4.82e-15 -16.782
HMC_vs_DEMetro_Z 0.3 -55.472 8.06e-15 -16.013
HMC_vs_DEMetro_Z 0.5 -39.117 3.69e-13 -11.292
HMC_vs_DEMetro_Z 0.9 -61.519 2.59e-15 -17.759
HMC_vs_DEMetro_Z 0.99 -36.206 8.59e-13 -10.452
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.013 0.015 0.002 -1.163
HMC 0.3 0.017 0.014 0.001 1.650
HMC 0.5 0.022 0.014 0.003 2.299
HMC 0.9 0.045 0.015 0.007 4.294
HMC 0.99 0.078 0.012 0.006 10.975
SMC 0.0 0.014 0.015 0.002 -0.241
SMC 0.3 0.014 0.014 0.001 -0.339
SMC 0.5 0.015 0.014 0.003 0.276
SMC 0.9 0.015 0.015 0.007 -0.073
SMC 0.99 0.015 0.012 0.006 0.445
Metro 0.0 0.023 0.015 0.002 5.621
Metro 0.3 0.043 0.014 0.001 20.933
Metro 0.5 0.067 0.014 0.003 15.608
Metro 0.9 0.227 0.015 0.007 30.523
Metro 0.99 0.376 0.012 0.006 60.370
DEMetro_Z 0.0 0.580 0.015 0.002 371.137
DEMetro_Z 0.3 0.583 0.014 0.001 419.725
DEMetro_Z 0.5 0.585 0.014 0.003 170.303
DEMetro_Z 0.9 0.575 0.015 0.007 80.900
DEMetro_Z 0.99 0.590 0.012 0.006 95.908
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -3.333 0.00341 -1.165
HMC 0.3 0.612 0.552 0.668
HMC 0.5 2.692 0.017 2.031
HMC 0.9 2.995 0.0103 2.942
HMC 0.99 3.387 0.00595 11.535
SMC 0.0 -0.828 0.416 -0.360
SMC 0.3 -0.184 0.856 -0.132
SMC 0.5 -1.384 0.183 -0.466
SMC 0.9 -0.181 0.858 -0.066
SMC 0.99 0.836 0.413 0.417
Metro 0.0 10.529 8.6e-10 3.862
Metro 0.3 4.283 0.00124 12.440
Metro 0.5 4.054 0.00187 17.440
Metro 0.9 4.483 0.000914 23.650
Metro 0.99 6.242 6.33e-05 185.089
DEMetro_Z 0.0 12.792 6.01e-08 3091.522
DEMetro_Z 0.3 17.701 1.97e-09 3389.717
DEMetro_Z 0.5 29.622 7.64e-12 1784.172
DEMetro_Z 0.9 27.867 1.48e-11 779.199
DEMetro_Z 0.99 20.930 3.28e-10 955.487
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -12.799 5.98e-08 -3.695
HMC_vs_DEMetro_Z 0.3 -17.705 1.97e-09 -5.111
HMC_vs_DEMetro_Z 0.5 -29.657 7.55e-12 -8.561
HMC_vs_DEMetro_Z 0.9 -27.514 1.71e-11 -7.943
HMC_vs_DEMetro_Z 0.99 -20.599 3.89e-10 -5.946
Metro_vs_SMC 0.0 12.326 8.83e-08 3.558
Metro_vs_SMC 0.3 4.653 0.000702 1.343
Metro_vs_SMC 0.5 4.127 0.00168 1.191
Metro_vs_SMC 0.9 4.502 0.000898 1.300
Metro_vs_SMC 0.99 6.265 6.13e-05 1.809
Metro_vs_DEMetro_Z 0.0 -12.774 6.1e-08 -3.688
Metro_vs_DEMetro_Z 0.3 -17.576 2.13e-09 -5.074
Metro_vs_DEMetro_Z 0.5 -29.206 8.93e-12 -8.431
Metro_vs_DEMetro_Z 0.9 -26.815 2.26e-11 -7.741
Metro_vs_DEMetro_Z 0.99 -17.293 2.53e-09 -4.992
HMC_vs_Metro 0.0 -15.747 6.83e-09 -4.546
HMC_vs_Metro 0.3 -3.778 0.00306 -1.091
HMC_vs_Metro 0.5 -3.357 0.0064 -0.969
HMC_vs_Metro 0.9 -3.992 0.00211 -1.152
HMC_vs_Metro 0.99 -5.977 9.22e-05 -1.726
HMC_vs_SMC 0.0 -2.993 0.0122 -0.864
HMC_vs_SMC 0.3 0.670 0.516 0.194
HMC_vs_SMC 0.5 3.246 0.00779 0.937
HMC_vs_SMC 0.9 3.232 0.00799 0.933
HMC_vs_SMC 0.99 3.212 0.00828 0.927
DEMetro_Z_vs_SMC 0.0 12.792 6.01e-08 3.693
DEMetro_Z_vs_SMC 0.3 17.704 1.97e-09 5.111
DEMetro_Z_vs_SMC 0.5 29.605 7.7e-12 8.546
DEMetro_Z_vs_SMC 0.9 27.970 1.43e-11 8.074
DEMetro_Z_vs_SMC 0.99 21.056 3.08e-10 6.078
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.019 0.023 0.003 -1.165
HMC 0.3 0.024 0.021 0.004 0.668
HMC 0.5 0.035 0.021 0.007 2.031
HMC 0.9 0.064 0.021 0.014 2.942
HMC 0.99 0.138 0.015 0.011 11.535
SMC 0.0 0.022 0.023 0.003 -0.360
SMC 0.3 0.021 0.021 0.004 -0.132
SMC 0.5 0.017 0.021 0.007 -0.466
SMC 0.9 0.020 0.021 0.014 -0.066
SMC 0.99 0.019 0.015 0.011 0.417
Metro 0.0 0.037 0.023 0.003 3.862
Metro 0.3 0.067 0.021 0.004 12.440
Metro 0.5 0.143 0.021 0.007 17.440
Metro 0.9 0.363 0.021 0.014 23.650
Metro 0.99 2.000 0.015 0.011 185.089
DEMetro_Z 0.0 10.734 0.023 0.003 3091.522
DEMetro_Z 0.3 12.523 0.021 0.004 3389.717
DEMetro_Z 0.5 12.488 0.021 0.007 1784.172
DEMetro_Z 0.9 11.274 0.021 0.014 779.199
DEMetro_Z 0.99 10.266 0.015 0.011 955.487
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 4.967 6.52e-05 2.302
HMC 0.3 4.081 0.000495 1.696
HMC 0.5 1.134 0.269 0.431
HMC 0.9 2.289 0.0419 4.509
HMC 0.99 2.785 0.0177 20.057
SMC 0.0 -0.134 0.895 -0.049
SMC 0.3 2.216 0.0376 0.852
SMC 0.5 0.375 0.712 0.128
SMC 0.9 -1.925 0.0714 -0.630
SMC 0.99 1.668 0.112 0.868
Metro 0.0 7.973 2.75e-07 4.532
Metro 0.3 9.261 8.55e-08 6.156
Metro 0.5 4.636 0.000539 5.678
Metro 0.9 8.093 4.92e-06 20.090
Metro 0.99 16.010 5.03e-09 64.671
DEMetro_Z 0.0 9.710 9.92e-07 4452.183
DEMetro_Z 0.3 11.326 2.1e-07 4643.030
DEMetro_Z 0.5 6.479 4.56e-05 1500.108
DEMetro_Z 0.9 8.628 3.16e-06 1149.339
DEMetro_Z 0.99 8.589 3.3e-06 1748.721
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 6.486 4.52e-05 1.872
HMC_vs_SMC 0.3 2.099 0.0597 0.606
HMC_vs_SMC 0.5 1.143 0.277 0.330
HMC_vs_SMC 0.9 2.570 0.0261 0.742
HMC_vs_SMC 0.99 2.691 0.021 0.777
Metro_vs_DEMetro_Z 0.0 -9.700 1e-06 -2.800
Metro_vs_DEMetro_Z 0.3 -11.308 2.14e-07 -3.264
Metro_vs_DEMetro_Z 0.5 -6.450 4.74e-05 -1.862
Metro_vs_DEMetro_Z 0.9 -8.594 3.29e-06 -2.481
Metro_vs_DEMetro_Z 0.99 -8.257 4.83e-06 -2.383
HMC_vs_Metro 0.0 -3.261 0.00759 -0.941
HMC_vs_Metro 0.3 -6.543 4.18e-05 -1.889
HMC_vs_Metro 0.5 -4.430 0.00101 -1.279
HMC_vs_Metro 0.9 -4.556 0.000822 -1.315
HMC_vs_Metro 0.99 -4.611 0.000751 -1.331
HMC_vs_DEMetro_Z 0.0 -9.705 9.97e-07 -2.802
HMC_vs_DEMetro_Z 0.3 -11.322 2.11e-07 -3.268
HMC_vs_DEMetro_Z 0.5 -6.477 4.57e-05 -1.870
HMC_vs_DEMetro_Z 0.9 -8.570 3.37e-06 -2.474
HMC_vs_DEMetro_Z 0.99 -8.448 3.88e-06 -2.439
Metro_vs_SMC 0.0 7.112 1.96e-05 2.053
Metro_vs_SMC 0.3 6.849 2.77e-05 1.977
Metro_vs_SMC 0.5 5.182 0.000303 1.496
Metro_vs_SMC 0.9 8.577 3.35e-06 2.476
Metro_vs_SMC 0.99 15.349 8.95e-09 4.431
DEMetro_Z_vs_SMC 0.0 9.707 9.94e-07 2.802
DEMetro_Z_vs_SMC 0.3 11.324 2.11e-07 3.269
DEMetro_Z_vs_SMC 0.5 6.478 4.57e-05 1.870
DEMetro_Z_vs_SMC 0.9 8.641 3.12e-06 2.494
DEMetro_Z_vs_SMC 0.99 8.580 3.34e-06 2.477
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.043 0.033 0.005 2.302
HMC 0.3 0.038 0.031 0.004 1.696
HMC 0.5 0.036 0.032 0.010 0.431
HMC 0.9 0.111 0.031 0.018 4.509
HMC 0.99 0.270 0.021 0.012 20.057
SMC 0.0 0.032 0.033 0.005 -0.049
SMC 0.3 0.034 0.031 0.004 0.852
SMC 0.5 0.033 0.032 0.010 0.128
SMC 0.9 0.020 0.031 0.018 -0.630
SMC 0.99 0.032 0.021 0.012 0.868
Metro 0.0 0.053 0.033 0.005 4.532
Metro 0.3 0.058 0.031 0.004 6.156
Metro 0.5 0.088 0.032 0.010 5.678
Metro 0.9 0.385 0.031 0.018 20.090
Metro 0.99 0.824 0.021 0.012 64.671
DEMetro_Z 0.0 20.304 0.033 0.005 4452.183
DEMetro_Z 0.3 20.562 0.031 0.004 4643.030
DEMetro_Z 0.5 14.855 0.032 0.010 1500.108
DEMetro_Z 0.9 20.259 0.031 0.018 1149.339
DEMetro_Z 0.99 21.733 0.021 0.012 1748.721
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 0.232 0.819 0.079
HMC 0.3 1.565 0.144 2.126
HMC 0.5 3.329 0.00513 2.923
HMC 0.9 4.059 0.00149 4.824
HMC 0.99 4.313 0.0012 16.696
SMC 0.0 -0.514 0.613 -0.241
SMC 0.3 0.317 0.756 0.267
SMC 0.5 -0.700 0.493 -0.233
SMC 0.9 -0.999 0.332 -0.328
SMC 0.99 1.473 0.155 0.622
Metro 0.0 12.263 4.73e-11 5.642
Metro 0.3 5.052 0.000359 20.068
Metro 0.5 4.180 0.00152 25.622
Metro 0.9 5.795 0.000117 30.546
Metro 0.99 6.713 3.32e-05 220.610
DEMetro_Z 0.0 13.047 4.9e-08 4573.180
DEMetro_Z 0.3 17.447 2.3e-09 6159.739
DEMetro_Z 0.5 28.146 1.33e-11 2801.409
DEMetro_Z 0.9 32.018 3.27e-12 948.719
DEMetro_Z 0.99 20.306 4.54e-10 1194.145
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -13.032 4.96e-08 -3.762
Metro_vs_DEMetro_Z 0.3 -17.338 2.46e-09 -5.005
Metro_vs_DEMetro_Z 0.5 -27.535 1.69e-11 -7.949
Metro_vs_DEMetro_Z 0.9 -30.820 4.97e-12 -8.897
Metro_vs_DEMetro_Z 0.99 -17.292 2.53e-09 -4.992
DEMetro_Z_vs_SMC 0.0 13.046 4.91e-08 3.766
DEMetro_Z_vs_SMC 0.3 17.444 2.3e-09 5.036
DEMetro_Z_vs_SMC 0.5 28.121 1.35e-11 8.118
DEMetro_Z_vs_SMC 0.9 32.068 3.23e-12 9.257
DEMetro_Z_vs_SMC 0.99 20.372 4.39e-10 5.881
HMC_vs_DEMetro_Z 0.0 -13.048 4.9e-08 -3.767
HMC_vs_DEMetro_Z 0.3 -17.447 2.3e-09 -5.036
HMC_vs_DEMetro_Z 0.5 -28.149 1.33e-11 -8.126
HMC_vs_DEMetro_Z 0.9 -31.589 3.8e-12 -9.119
HMC_vs_DEMetro_Z 0.99 -20.181 4.85e-10 -5.826
HMC_vs_Metro 0.0 -13.405 3.7e-08 -3.870
HMC_vs_Metro 0.3 -4.194 0.0015 -1.211
HMC_vs_Metro 0.5 -3.520 0.0048 -1.016
HMC_vs_Metro 0.9 -4.743 0.000606 -1.369
HMC_vs_Metro 0.99 -6.494 4.46e-05 -1.875
HMC_vs_SMC 0.0 0.994 0.342 0.287
HMC_vs_SMC 0.3 1.232 0.244 0.356
HMC_vs_SMC 0.5 3.521 0.00479 1.017
HMC_vs_SMC 0.9 4.387 0.00109 1.266
HMC_vs_SMC 0.99 4.271 0.00132 1.233
Metro_vs_SMC 0.0 14.758 1.35e-08 4.260
Metro_vs_SMC 0.3 5.348 0.000235 1.544
Metro_vs_SMC 0.5 4.217 0.00144 1.217
Metro_vs_SMC 0.9 5.833 0.000114 1.684
Metro_vs_SMC 0.99 6.733 3.23e-05 1.944
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.029 0.029 0.002 0.079
HMC 0.3 0.031 0.028 0.002 2.126
HMC 0.5 0.037 0.027 0.004 2.923
HMC 0.9 0.074 0.027 0.010 4.824
HMC 0.99 0.143 0.021 0.007 16.696
SMC 0.0 0.029 0.029 0.002 -0.241
SMC 0.3 0.028 0.028 0.002 0.267
SMC 0.5 0.026 0.027 0.004 -0.233
SMC 0.9 0.024 0.027 0.010 -0.328
SMC 0.99 0.025 0.021 0.007 0.622
Metro 0.0 0.040 0.029 0.002 5.642
Metro 0.3 0.062 0.028 0.002 20.068
Metro 0.5 0.121 0.027 0.004 25.622
Metro 0.9 0.326 0.027 0.010 30.546
Metro 0.99 1.632 0.021 0.007 220.610
DEMetro_Z 0.0 9.039 0.029 0.002 4573.180
DEMetro_Z 0.3 10.559 0.028 0.002 6159.739
DEMetro_Z 0.5 10.298 0.027 0.004 2801.409
DEMetro_Z 0.9 9.327 0.027 0.010 948.719
DEMetro_Z 0.99 8.741 0.021 0.007 1194.145
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -1.705 0.103 -0.641
HMC 0.3 1.228 0.243 1.598
HMC 0.5 2.646 0.0187 2.030
HMC 0.9 4.686 0.000409 4.470
HMC 0.99 4.521 0.000829 13.242
SMC 0.0 -1.571 0.131 -0.662
SMC 0.3 -0.086 0.932 -0.071
SMC 0.5 -0.559 0.582 -0.196
SMC 0.9 -1.511 0.152 -0.470
SMC 0.99 1.340 0.194 0.569
Metro 0.0 11.967 4.51e-11 5.081
Metro 0.3 5.034 0.000365 16.815
Metro 0.5 4.153 0.00158 18.663
Metro 0.9 7.951 6.42e-06 29.591
Metro 0.99 16.565 3.88e-09 142.221
DEMetro_Z 0.0 55.457 7.79e-15 595.479
DEMetro_Z 0.3 38.420 4.44e-13 686.109
DEMetro_Z 0.5 26.050 3.02e-11 292.382
DEMetro_Z 0.9 67.878 2.65e-16 135.498
DEMetro_Z 0.99 55.147 4.93e-15 154.305
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 55.568 7.91e-15 16.041
DEMetro_Z_vs_SMC 0.3 38.138 4.87e-13 11.010
DEMetro_Z_vs_SMC 0.5 25.929 3.25e-11 7.485
DEMetro_Z_vs_SMC 0.9 69.347 6.96e-16 20.019
DEMetro_Z_vs_SMC 0.99 56.318 6.83e-15 16.258
HMC_vs_Metro 0.0 -16.765 3.51e-09 -4.840
HMC_vs_Metro 0.3 -4.150 0.00162 -1.198
HMC_vs_Metro 0.5 -3.487 0.00508 -1.007
HMC_vs_Metro 0.9 -6.673 3.5e-05 -1.926
HMC_vs_Metro 0.99 -15.726 6.92e-09 -4.540
Metro_vs_DEMetro_Z 0.0 -55.197 8.51e-15 -15.934
Metro_vs_DEMetro_Z 0.3 -35.362 1.11e-12 -10.208
Metro_vs_DEMetro_Z 0.5 -22.553 1.47e-10 -6.510
Metro_vs_DEMetro_Z 0.9 -25.801 3.43e-11 -7.448
Metro_vs_DEMetro_Z 0.99 -1.300 0.22 -0.375
HMC_vs_SMC 0.0 0.099 0.923 0.029
HMC_vs_SMC 0.3 1.146 0.276 0.331
HMC_vs_SMC 0.5 2.865 0.0154 0.827
HMC_vs_SMC 0.9 5.325 0.000243 1.537
HMC_vs_SMC 0.99 4.510 0.000887 1.302
Metro_vs_SMC 0.0 17.847 1.81e-09 5.152
Metro_vs_SMC 0.3 5.278 0.000261 1.524
Metro_vs_SMC 0.5 4.177 0.00154 1.206
Metro_vs_SMC 0.9 7.988 6.63e-06 2.306
Metro_vs_SMC 0.99 16.840 3.35e-09 4.861
HMC_vs_DEMetro_Z 0.0 -55.588 7.88e-15 -16.047
HMC_vs_DEMetro_Z 0.3 -38.259 4.7e-13 -11.045
HMC_vs_DEMetro_Z 0.5 -25.928 3.25e-11 -7.485
HMC_vs_DEMetro_Z 0.9 -61.963 2.39e-15 -17.887
HMC_vs_DEMetro_Z 0.99 -29.993 6.68e-12 -8.658
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.014 0.015 0.002 -0.641
HMC 0.3 0.016 0.014 0.001 1.598
HMC 0.5 0.021 0.014 0.003 2.030
HMC 0.9 0.046 0.015 0.007 4.470
HMC 0.99 0.092 0.012 0.006 13.242
SMC 0.0 0.014 0.015 0.002 -0.662
SMC 0.3 0.014 0.014 0.001 -0.071
SMC 0.5 0.014 0.014 0.003 -0.196
SMC 0.9 0.012 0.015 0.007 -0.470
SMC 0.99 0.016 0.012 0.006 0.569
Metro 0.0 0.022 0.015 0.002 5.081
Metro 0.3 0.037 0.014 0.001 16.815
Metro 0.5 0.077 0.014 0.003 18.663
Metro 0.9 0.220 0.015 0.007 29.591
Metro 0.99 0.868 0.012 0.006 142.221
DEMetro_Z 0.0 0.921 0.015 0.002 595.479
DEMetro_Z 0.3 0.945 0.014 0.001 686.109
DEMetro_Z 0.5 0.995 0.014 0.003 292.382
DEMetro_Z 0.9 0.953 0.015 0.007 135.498
DEMetro_Z 0.99 0.941 0.012 0.006 154.305
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Forest & Ridge Plots
Pooled
0.0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.9 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.99 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0.0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.9 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.99 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.99
Chain
0.0
0.3
0.5
0.9
0.99

Vary_Correlation_with_heavy_Tails (MvStudentT, correlation, 12 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -1.174 0.253 -0.476
HMC 0.3 0.234 0.817 0.106
HMC 0.5 1.349 0.191 0.554
HMC 0.9 2.626 0.021 2.645
HMC 0.99 0.608 0.551 0.205
SMC 0.0 -0.226 0.823 -0.079
SMC 0.3 -0.765 0.453 -0.281
SMC 0.5 -0.291 0.774 -0.106
SMC 0.9 0.965 0.348 0.574
SMC 0.99 -0.070 0.945 -0.027
Metro 0.0 1.792 0.0886 0.907
Metro 0.3 3.263 0.00388 1.601
Metro 0.5 3.044 0.0105 4.959
Metro 0.9 2.775 0.0175 5.611
Metro 0.99 4.358 0.000951 6.360
DEMetro_Z 0.0 4.120 0.000671 2.379
DEMetro_Z 0.3 3.073 0.00752 2.123
DEMetro_Z 0.5 3.486 0.00218 1.589
DEMetro_Z 0.9 2.208 0.0486 5.031
DEMetro_Z 0.99 1.412 0.174 0.721
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -4.716 0.000633 -1.362
HMC_vs_DEMetro_Z 0.3 -2.394 0.0356 -0.691
HMC_vs_DEMetro_Z 0.5 -2.937 0.0135 -0.848
HMC_vs_DEMetro_Z 0.9 -1.471 0.169 -0.425
HMC_vs_DEMetro_Z 0.99 -1.040 0.321 -0.300
Metro_vs_SMC 0.0 2.349 0.0386 0.678
Metro_vs_SMC 0.3 5.325 0.000243 1.537
Metro_vs_SMC 0.5 3.119 0.00976 0.900
Metro_vs_SMC 0.9 2.480 0.0306 0.716
Metro_vs_SMC 0.99 4.235 0.0014 1.223
Metro_vs_DEMetro_Z 0.0 -2.100 0.0596 -0.606
Metro_vs_DEMetro_Z 0.3 -0.585 0.57 -0.169
Metro_vs_DEMetro_Z 0.5 1.981 0.0732 0.572
Metro_vs_DEMetro_Z 0.9 0.174 0.865 0.050
Metro_vs_DEMetro_Z 0.99 3.477 0.00518 1.004
HMC_vs_Metro 0.0 -3.108 0.00996 -0.897
HMC_vs_Metro 0.3 -2.822 0.0166 -0.815
HMC_vs_Metro 0.5 -2.639 0.0231 -0.762
HMC_vs_Metro 0.9 -1.497 0.162 -0.432
HMC_vs_Metro 0.99 -4.245 0.00138 -1.225
HMC_vs_SMC 0.0 -1.611 0.135 -0.465
HMC_vs_SMC 0.3 0.802 0.439 0.232
HMC_vs_SMC 0.5 1.881 0.0866 0.543
HMC_vs_SMC 0.9 2.083 0.0614 0.601
HMC_vs_SMC 0.99 0.666 0.519 0.192
DEMetro_Z_vs_SMC 0.0 4.950 0.000436 1.429
DEMetro_Z_vs_SMC 0.3 3.691 0.00356 1.065
DEMetro_Z_vs_SMC 0.5 4.222 0.00143 1.219
DEMetro_Z_vs_SMC 0.9 2.067 0.0631 0.597
DEMetro_Z_vs_SMC 0.99 1.510 0.159 0.436
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.053 0.072 0.040 -0.476
HMC 0.3 0.061 0.058 0.035 0.106
HMC 0.5 0.075 0.054 0.037 0.554
HMC 0.9 0.121 0.046 0.028 2.645
HMC 0.99 0.088 0.070 0.087 0.205
SMC 0.0 0.069 0.072 0.040 -0.079
SMC 0.3 0.048 0.058 0.035 -0.281
SMC 0.5 0.050 0.054 0.037 -0.106
SMC 0.9 0.062 0.046 0.028 0.574
SMC 0.99 0.068 0.070 0.087 -0.027
Metro 0.0 0.108 0.072 0.040 0.907
Metro 0.3 0.113 0.058 0.035 1.601
Metro 0.5 0.239 0.054 0.037 4.959
Metro 0.9 0.205 0.046 0.028 5.611
Metro 0.99 0.623 0.070 0.087 6.360
DEMetro_Z 0.0 0.167 0.072 0.040 2.379
DEMetro_Z 0.3 0.131 0.058 0.035 2.123
DEMetro_Z 0.5 0.113 0.054 0.037 1.589
DEMetro_Z 0.9 0.189 0.046 0.028 5.031
DEMetro_Z 0.99 0.133 0.070 0.087 0.721
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.169 0.867 -0.066
HMC 0.3 -1.109 0.285 -0.348
HMC 0.5 0.798 0.435 0.446
HMC 0.9 1.673 0.117 1.421
HMC 0.99 0.800 0.433 0.286
SMC 0.0 -0.187 0.853 -0.070
SMC 0.3 -1.649 0.124 -0.495
SMC 0.5 -0.881 0.39 -0.295
SMC 0.9 1.200 0.248 0.826
SMC 0.99 0.852 0.408 0.671
Metro 0.0 -0.134 0.894 -0.053
Metro 0.3 -1.447 0.171 -0.442
Metro 0.5 0.070 0.945 0.029
Metro 0.9 1.692 0.113 1.410
Metro 0.99 1.395 0.177 0.523
DEMetro_Z 0.0 -0.045 0.965 -0.017
DEMetro_Z 0.3 -0.329 0.746 -0.112
DEMetro_Z 0.5 0.235 0.817 0.084
DEMetro_Z 0.9 2.071 0.0577 1.769
DEMetro_Z 0.99 0.856 0.403 0.296
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 0.092 0.929 0.026
HMC_vs_SMC 0.3 1.029 0.325 0.297
HMC_vs_SMC 0.5 1.576 0.143 0.455
HMC_vs_SMC 0.9 1.494 0.163 0.431
HMC_vs_SMC 0.99 -0.498 0.628 -0.144
Metro_vs_DEMetro_Z 0.0 -1.037 0.322 -0.299
Metro_vs_DEMetro_Z 0.3 -1.653 0.127 -0.477
Metro_vs_DEMetro_Z 0.5 -0.182 0.859 -0.053
Metro_vs_DEMetro_Z 0.9 -2.153 0.0543 -0.622
Metro_vs_DEMetro_Z 0.99 1.046 0.318 0.302
HMC_vs_Metro 0.0 -0.713 0.491 -0.206
HMC_vs_Metro 0.3 0.805 0.438 0.232
HMC_vs_Metro 0.5 0.653 0.527 0.188
HMC_vs_Metro 0.9 0.028 0.978 0.008
HMC_vs_Metro 0.99 -0.832 0.423 -0.240
HMC_vs_DEMetro_Z 0.0 -1.288 0.224 -0.372
HMC_vs_DEMetro_Z 0.3 -1.307 0.218 -0.377
HMC_vs_DEMetro_Z 0.5 0.683 0.509 0.197
HMC_vs_DEMetro_Z 0.9 -0.982 0.347 -0.283
HMC_vs_DEMetro_Z 0.99 -0.042 0.967 -0.012
Metro_vs_SMC 0.0 0.385 0.707 0.111
Metro_vs_SMC 0.3 0.393 0.702 0.113
Metro_vs_SMC 0.5 1.097 0.296 0.317
Metro_vs_SMC 0.9 2.372 0.0371 0.685
Metro_vs_SMC 0.99 -0.196 0.848 -0.057
DEMetro_Z_vs_SMC 0.0 1.064 0.31 0.307
DEMetro_Z_vs_SMC 0.3 1.852 0.091 0.535
DEMetro_Z_vs_SMC 0.5 1.565 0.146 0.452
DEMetro_Z_vs_SMC 0.9 3.666 0.00372 1.058
DEMetro_Z_vs_SMC 0.99 -0.544 0.597 -0.157
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 7.776 8.779 15.112 -0.066
HMC 0.3 3.105 4.691 4.555 -0.348
HMC 0.5 4.549 3.238 2.938 0.446
HMC 0.9 6.358 2.593 2.648 1.421
HMC 0.99 3.695 2.752 3.294 0.286
SMC 0.0 7.719 8.779 15.112 -0.070
SMC 0.3 2.437 4.691 4.555 -0.495
SMC 0.5 2.372 3.238 2.938 -0.295
SMC 0.9 4.782 2.593 2.648 0.826
SMC 0.99 4.962 2.752 3.294 0.671
Metro 0.0 7.985 8.779 15.112 -0.053
Metro 0.3 2.680 4.691 4.555 -0.442
Metro 0.5 3.324 3.238 2.938 0.029
Metro 0.9 6.328 2.593 2.648 1.410
Metro 0.99 4.475 2.752 3.294 0.523
DEMetro_Z 0.0 8.515 8.779 15.112 -0.017
DEMetro_Z 0.3 4.181 4.691 4.555 -0.112
DEMetro_Z 0.5 3.485 3.238 2.938 0.084
DEMetro_Z 0.9 7.278 2.593 2.648 1.769
DEMetro_Z 0.99 3.728 2.752 3.294 0.296
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 0.844 0.409 0.411
HMC 0.3 2.033 0.0615 1.675
HMC 0.5 3.414 0.00491 3.995
HMC 0.9 2.884 0.0138 4.140
HMC 0.99 2.227 0.037 1.023
SMC 0.0 1.271 0.217 0.534
SMC 0.3 -0.202 0.842 -0.096
SMC 0.5 0.730 0.473 0.264
SMC 0.9 1.709 0.102 0.800
SMC 0.99 1.272 0.22 0.735
Metro 0.0 4.696 0.00018 2.636
Metro 0.3 5.335 0.000132 5.190
Metro 0.5 3.704 0.00321 6.850
Metro 0.9 4.803 0.000464 7.933
Metro 0.99 6.244 4.25e-05 8.534
DEMetro_Z 0.0 5.613 4.31e-05 3.837
DEMetro_Z 0.3 5.131 0.000271 8.587
DEMetro_Z 0.5 10.539 7e-09 6.344
DEMetro_Z 0.9 4.241 0.00126 8.373
DEMetro_Z 0.99 3.577 0.00178 1.652
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -2.304 0.0417 -0.665
Metro_vs_DEMetro_Z 0.3 -1.611 0.136 -0.465
Metro_vs_DEMetro_Z 0.5 0.258 0.801 0.075
Metro_vs_DEMetro_Z 0.9 -0.158 0.877 -0.046
Metro_vs_DEMetro_Z 0.99 4.948 0.000437 1.428
DEMetro_Z_vs_SMC 0.0 6.876 2.67e-05 1.985
DEMetro_Z_vs_SMC 0.3 4.825 0.000531 1.393
DEMetro_Z_vs_SMC 0.5 9.768 9.35e-07 2.820
DEMetro_Z_vs_SMC 0.9 3.702 0.00349 1.069
DEMetro_Z_vs_SMC 0.99 1.583 0.142 0.457
HMC_vs_DEMetro_Z 0.0 -5.796 0.00012 -1.673
HMC_vs_DEMetro_Z 0.3 -3.562 0.00445 -1.028
HMC_vs_DEMetro_Z 0.5 -2.116 0.058 -0.611
HMC_vs_DEMetro_Z 0.9 -5.893 0.000104 -1.701
HMC_vs_DEMetro_Z 0.99 -1.000 0.339 -0.289
HMC_vs_Metro 0.0 -6.066 8.12e-05 -1.751
HMC_vs_Metro 0.3 -2.957 0.013 -0.854
HMC_vs_Metro 0.5 -1.200 0.256 -0.346
HMC_vs_Metro 0.9 -1.584 0.142 -0.457
HMC_vs_Metro 0.99 -5.198 0.000295 -1.501
HMC_vs_SMC 0.0 -0.459 0.655 -0.132
HMC_vs_SMC 0.3 2.218 0.0485 0.640
HMC_vs_SMC 0.5 3.307 0.00699 0.955
HMC_vs_SMC 0.9 2.286 0.0431 0.660
HMC_vs_SMC 0.99 0.423 0.68 0.122
Metro_vs_SMC 0.0 5.839 0.000113 1.686
Metro_vs_SMC 0.3 5.167 0.00031 1.492
Metro_vs_SMC 0.5 3.861 0.00265 1.114
Metro_vs_SMC 0.9 4.554 0.000824 1.315
Metro_vs_SMC 0.99 5.339 0.000238 1.541
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.138 0.122 0.038 0.411
HMC 0.3 0.152 0.119 0.020 1.675
HMC 0.5 0.205 0.103 0.025 3.995
HMC 0.9 0.210 0.099 0.027 4.140
HMC 0.99 0.187 0.111 0.074 1.023
SMC 0.0 0.142 0.122 0.038 0.534
SMC 0.3 0.117 0.119 0.020 -0.096
SMC 0.5 0.110 0.103 0.025 0.264
SMC 0.9 0.121 0.099 0.027 0.800
SMC 0.99 0.166 0.111 0.074 0.735
Metro 0.0 0.222 0.122 0.038 2.636
Metro 0.3 0.220 0.119 0.020 5.190
Metro 0.5 0.278 0.103 0.025 6.850
Metro 0.9 0.312 0.099 0.027 7.933
Metro 0.99 0.747 0.111 0.074 8.534
DEMetro_Z 0.0 0.267 0.122 0.038 3.837
DEMetro_Z 0.3 0.287 0.119 0.020 8.587
DEMetro_Z 0.5 0.265 0.103 0.025 6.344
DEMetro_Z 0.9 0.324 0.099 0.027 8.373
DEMetro_Z 0.99 0.234 0.111 0.074 1.652
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 1.505 0.147 0.694
HMC 0.3 2.533 0.0226 1.753
HMC 0.5 2.269 0.0433 4.324
HMC 0.9 2.712 0.0181 2.925
HMC 0.99 2.687 0.0195 3.360
SMC 0.0 2.180 0.0409 1.015
SMC 0.3 2.113 0.0496 1.262
SMC 0.5 1.202 0.242 0.500
SMC 0.9 1.180 0.253 0.637
SMC 0.99 2.313 0.0394 3.336
Metro 0.0 5.926 3.99e-05 5.100
Metro 0.3 5.709 0.000108 9.449
Metro 0.5 6.220 2.69e-05 5.659
Metro 0.9 4.763 0.000517 9.062
Metro 0.99 6.946 2.37e-05 38.614
DEMetro_Z 0.0 4.218 0.00123 6.440
DEMetro_Z 0.3 7.502 7.37e-06 10.597
DEMetro_Z 0.5 8.862 6.63e-07 8.566
DEMetro_Z 0.9 2.871 0.0149 8.111
DEMetro_Z 0.99 4.737 0.000432 5.402
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 3.809 0.0029 1.100
DEMetro_Z_vs_SMC 0.3 5.621 0.000155 1.623
DEMetro_Z_vs_SMC 0.5 8.605 3.24e-06 2.484
DEMetro_Z_vs_SMC 0.9 2.791 0.0176 0.806
DEMetro_Z_vs_SMC 0.99 1.062 0.311 0.307
HMC_vs_Metro 0.0 -4.606 0.000757 -1.330
HMC_vs_Metro 0.3 -4.713 0.000637 -1.360
HMC_vs_Metro 0.5 -0.585 0.57 -0.169
HMC_vs_Metro 0.9 -2.533 0.0278 -0.731
HMC_vs_Metro 0.99 -6.907 2.57e-05 -1.994
Metro_vs_DEMetro_Z 0.0 -0.838 0.42 -0.242
Metro_vs_DEMetro_Z 0.3 -0.579 0.574 -0.167
Metro_vs_DEMetro_Z 0.5 -2.059 0.064 -0.594
Metro_vs_DEMetro_Z 0.9 0.260 0.799 0.075
Metro_vs_DEMetro_Z 0.99 6.282 5.98e-05 1.814
HMC_vs_SMC 0.0 -0.762 0.462 -0.220
HMC_vs_SMC 0.3 0.592 0.566 0.171
HMC_vs_SMC 0.5 1.898 0.0843 0.548
HMC_vs_SMC 0.9 2.455 0.0319 0.709
HMC_vs_SMC 0.99 0.011 0.991 0.003
Metro_vs_SMC 0.0 4.402 0.00106 1.271
Metro_vs_SMC 0.3 4.466 0.000954 1.289
Metro_vs_SMC 0.5 5.548 0.000173 1.601
Metro_vs_SMC 0.9 4.400 0.00106 1.270
Metro_vs_SMC 0.99 5.416 0.000212 1.563
HMC_vs_DEMetro_Z 0.0 -3.447 0.00546 -0.995
HMC_vs_DEMetro_Z 0.3 -5.750 0.000128 -1.660
HMC_vs_DEMetro_Z 0.5 -1.990 0.072 -0.575
HMC_vs_DEMetro_Z 0.9 -2.787 0.0177 -0.805
HMC_vs_DEMetro_Z 0.99 -1.118 0.287 -0.323
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.017 0.014 0.004 0.694
HMC 0.3 0.019 0.014 0.003 1.753
HMC 0.5 0.029 0.014 0.004 4.324
HMC 0.9 0.030 0.015 0.005 2.925
HMC 0.99 0.030 0.015 0.004 3.360
SMC 0.0 0.019 0.014 0.004 1.015
SMC 0.3 0.018 0.014 0.003 1.262
SMC 0.5 0.015 0.014 0.004 0.500
SMC 0.9 0.018 0.015 0.005 0.637
SMC 0.99 0.029 0.015 0.004 3.336
Metro 0.0 0.037 0.014 0.004 5.100
Metro 0.3 0.042 0.014 0.003 9.449
Metro 0.5 0.034 0.014 0.004 5.659
Metro 0.9 0.063 0.015 0.005 9.062
Metro 0.99 0.182 0.015 0.004 38.614
DEMetro_Z 0.0 0.043 0.014 0.004 6.440
DEMetro_Z 0.3 0.046 0.014 0.003 10.597
DEMetro_Z 0.5 0.044 0.014 0.004 8.566
DEMetro_Z 0.9 0.058 0.015 0.005 8.111
DEMetro_Z 0.99 0.038 0.015 0.004 5.402
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.607 0.551 -0.218
HMC 0.3 -0.079 0.938 -0.034
HMC 0.5 0.599 0.558 0.407
HMC 0.9 2.118 0.048 1.160
HMC 0.99 -0.069 0.946 -0.023
SMC 0.0 -1.130 0.274 -0.377
SMC 0.3 0.169 0.867 0.064
SMC 0.5 0.277 0.785 0.136
SMC 0.9 -0.531 0.601 -0.212
SMC 0.99 1.091 0.287 0.490
Metro 0.0 2.082 0.0496 0.948
Metro 0.3 1.862 0.0881 3.366
Metro 0.5 2.335 0.0315 1.330
Metro 0.9 3.784 0.0028 7.240
Metro 0.99 4.313 0.000972 5.482
DEMetro_Z 0.0 1.519 0.154 1.875
DEMetro_Z 0.3 2.062 0.0612 2.634
DEMetro_Z 0.5 4.045 0.000722 2.191
DEMetro_Z 0.9 1.992 0.07 3.073
DEMetro_Z 0.99 0.841 0.409 0.349
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -1.783 0.102 -0.515
HMC_vs_DEMetro_Z 0.3 -2.060 0.0639 -0.595
HMC_vs_DEMetro_Z 0.5 -2.485 0.0303 -0.717
HMC_vs_DEMetro_Z 0.9 -1.190 0.259 -0.344
HMC_vs_DEMetro_Z 0.99 -0.919 0.378 -0.265
Metro_vs_SMC 0.0 3.947 0.00229 1.139
Metro_vs_SMC 0.3 1.784 0.102 0.515
Metro_vs_SMC 0.5 1.614 0.135 0.466
Metro_vs_SMC 0.9 3.709 0.00345 1.071
Metro_vs_SMC 0.99 3.582 0.00431 1.034
Metro_vs_DEMetro_Z 0.0 -0.711 0.492 -0.205
Metro_vs_DEMetro_Z 0.3 0.331 0.747 0.096
Metro_vs_DEMetro_Z 0.5 -1.840 0.0928 -0.531
Metro_vs_DEMetro_Z 0.9 1.531 0.154 0.442
Metro_vs_DEMetro_Z 0.99 3.614 0.00407 1.043
HMC_vs_Metro 0.0 -3.136 0.00948 -0.905
HMC_vs_Metro 0.3 -1.836 0.0935 -0.530
HMC_vs_Metro 0.5 -1.398 0.19 -0.404
HMC_vs_Metro 0.9 -3.068 0.0107 -0.886
HMC_vs_Metro 0.99 -4.413 0.00104 -1.274
HMC_vs_SMC 0.0 0.531 0.606 0.153
HMC_vs_SMC 0.3 -0.233 0.82 -0.067
HMC_vs_SMC 0.5 0.350 0.733 0.101
HMC_vs_SMC 0.9 2.562 0.0264 0.740
HMC_vs_SMC 0.99 -1.347 0.205 -0.389
DEMetro_Z_vs_SMC 0.0 1.908 0.0829 0.551
DEMetro_Z_vs_SMC 0.3 1.932 0.0795 0.558
DEMetro_Z_vs_SMC 0.5 3.180 0.00876 0.918
DEMetro_Z_vs_SMC 0.9 2.439 0.0329 0.704
DEMetro_Z_vs_SMC 0.99 -0.328 0.749 -0.095
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.063 0.072 0.040 -0.218
HMC 0.3 0.056 0.058 0.035 -0.034
HMC 0.5 0.069 0.054 0.037 0.407
HMC 0.9 0.079 0.046 0.028 1.160
HMC 0.99 0.068 0.070 0.087 -0.023
SMC 0.0 0.057 0.072 0.040 -0.377
SMC 0.3 0.060 0.058 0.035 0.064
SMC 0.5 0.059 0.054 0.037 0.136
SMC 0.9 0.040 0.046 0.028 -0.212
SMC 0.99 0.113 0.070 0.087 0.490
Metro 0.0 0.110 0.072 0.040 0.948
Metro 0.3 0.174 0.058 0.035 3.366
Metro 0.5 0.104 0.054 0.037 1.330
Metro 0.9 0.251 0.046 0.028 7.240
Metro 0.99 0.547 0.070 0.087 5.482
DEMetro_Z 0.0 0.147 0.072 0.040 1.875
DEMetro_Z 0.3 0.148 0.058 0.035 2.634
DEMetro_Z 0.5 0.136 0.054 0.037 2.191
DEMetro_Z 0.9 0.133 0.046 0.028 3.073
DEMetro_Z 0.99 0.100 0.070 0.087 0.349
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.148 0.884 -0.055
HMC 0.3 -1.972 0.072 -0.583
HMC 0.5 0.857 0.409 1.900
HMC 0.9 1.653 0.121 1.408
HMC 0.99 0.682 0.503 0.262
SMC 0.0 0.002 0.998 0.001
SMC 0.3 0.007 0.994 0.004
SMC 0.5 0.961 0.357 10.679
SMC 0.9 1.263 0.227 0.993
SMC 0.99 0.805 0.431 0.440
Metro 0.0 -0.176 0.862 -0.067
Metro 0.3 0.345 0.734 0.199
Metro 0.5 -0.665 0.515 -0.222
Metro 0.9 2.121 0.0523 1.748
Metro 0.99 1.333 0.197 0.484
DEMetro_Z 0.0 0.048 0.962 0.019
DEMetro_Z 0.3 -0.096 0.925 -0.045
DEMetro_Z 0.5 0.156 0.878 0.049
DEMetro_Z 0.9 2.457 0.0286 2.354
DEMetro_Z 0.99 0.750 0.462 0.270
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 -0.620 0.548 -0.179
HMC_vs_SMC 0.3 -1.022 0.329 -0.295
HMC_vs_SMC 0.5 -0.762 0.462 -0.220
HMC_vs_SMC 0.9 2.240 0.0467 0.647
HMC_vs_SMC 0.99 -0.290 0.777 -0.084
Metro_vs_DEMetro_Z 0.0 -3.537 0.00466 -1.021
Metro_vs_DEMetro_Z 0.3 0.361 0.725 0.104
Metro_vs_DEMetro_Z 0.5 -3.009 0.0119 -0.869
Metro_vs_DEMetro_Z 0.9 -0.938 0.368 -0.271
Metro_vs_DEMetro_Z 0.99 1.255 0.235 0.362
HMC_vs_Metro 0.0 0.202 0.844 0.058
HMC_vs_Metro 0.3 -1.526 0.155 -0.441
HMC_vs_Metro 0.5 0.962 0.357 0.278
HMC_vs_Metro 0.9 -1.227 0.246 -0.354
HMC_vs_Metro 0.99 -0.787 0.448 -0.227
HMC_vs_DEMetro_Z 0.0 -1.349 0.205 -0.389
HMC_vs_DEMetro_Z 0.3 -1.555 0.148 -0.449
HMC_vs_DEMetro_Z 0.5 0.849 0.414 0.245
HMC_vs_DEMetro_Z 0.9 -1.434 0.179 -0.414
HMC_vs_DEMetro_Z 0.99 -0.029 0.977 -0.008
Metro_vs_SMC 0.0 -1.061 0.311 -0.306
Metro_vs_SMC 0.3 0.236 0.818 0.068
Metro_vs_SMC 0.5 -0.982 0.347 -0.284
Metro_vs_SMC 0.9 3.894 0.0025 1.124
Metro_vs_SMC 0.99 0.089 0.93 0.026
DEMetro_Z_vs_SMC 0.0 0.292 0.776 0.084
DEMetro_Z_vs_SMC 0.3 -0.073 0.943 -0.021
DEMetro_Z_vs_SMC 0.5 -0.958 0.358 -0.277
DEMetro_Z_vs_SMC 0.9 2.035 0.0666 0.588
DEMetro_Z_vs_SMC 0.99 -0.341 0.739 -0.099
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 7.948 8.779 15.112 -0.055
HMC 0.3 2.035 4.691 4.555 -0.583
HMC 0.5 8.820 3.238 2.938 1.900
HMC 0.9 6.321 2.593 2.648 1.408
HMC 0.99 3.615 2.752 3.294 0.262
SMC 0.0 8.792 8.779 15.112 0.001
SMC 0.3 4.711 4.691 4.555 0.004
SMC 0.5 34.612 3.238 2.938 10.679
SMC 0.9 5.224 2.593 2.648 0.993
SMC 0.99 4.200 2.752 3.294 0.440
Metro 0.0 7.764 8.779 15.112 -0.067
Metro 0.3 5.596 4.691 4.555 0.199
Metro 0.5 2.585 3.238 2.938 -0.222
Metro 0.9 7.223 2.593 2.648 1.748
Metro 0.99 4.348 2.752 3.294 0.484
DEMetro_Z 0.0 9.060 8.779 15.112 0.019
DEMetro_Z 0.3 4.486 4.691 4.555 -0.045
DEMetro_Z 0.5 3.382 3.238 2.938 0.049
DEMetro_Z 0.9 8.829 2.593 2.648 2.354
DEMetro_Z 0.99 3.641 2.752 3.294 0.270
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 1.056 0.302 0.430
HMC 0.3 0.711 0.488 0.510
HMC 0.5 1.727 0.11 2.603
HMC 0.9 5.886 1.12e-05 3.074
HMC 0.99 2.170 0.0414 0.824
SMC 0.0 0.396 0.696 0.180
SMC 0.3 -0.069 0.946 -0.035
SMC 0.5 1.287 0.221 1.333
SMC 0.9 0.379 0.709 0.142
SMC 0.99 1.059 0.302 0.487
Metro 0.0 3.909 0.000855 1.903
Metro 0.3 2.678 0.0211 7.315
Metro 0.5 6.626 1.95e-06 3.304
Metro 0.9 6.106 5.85e-05 9.905
Metro 0.99 7.875 3.15e-06 8.560
DEMetro_Z 0.0 3.597 0.00345 4.109
DEMetro_Z 0.3 4.131 0.00152 7.812
DEMetro_Z 0.5 10.965 4.39e-10 5.163
DEMetro_Z 0.9 3.017 0.0112 6.197
DEMetro_Z 0.99 5.066 4.58e-05 1.984
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -1.951 0.077 -0.563
Metro_vs_DEMetro_Z 0.3 -0.140 0.891 -0.040
Metro_vs_DEMetro_Z 0.5 -3.939 0.00231 -1.137
Metro_vs_DEMetro_Z 0.9 1.373 0.197 0.396
Metro_vs_DEMetro_Z 0.99 5.965 9.38e-05 1.722
DEMetro_Z_vs_SMC 0.0 3.501 0.00496 1.011
DEMetro_Z_vs_SMC 0.3 4.003 0.00208 1.156
DEMetro_Z_vs_SMC 0.5 3.859 0.00266 1.114
DEMetro_Z_vs_SMC 0.9 3.043 0.0112 0.878
DEMetro_Z_vs_SMC 0.99 3.271 0.00745 0.944
HMC_vs_DEMetro_Z 0.0 -3.181 0.00874 -0.918
HMC_vs_DEMetro_Z 0.3 -3.645 0.00385 -1.052
HMC_vs_DEMetro_Z 0.5 -1.718 0.114 -0.496
HMC_vs_DEMetro_Z 0.9 -1.502 0.161 -0.434
HMC_vs_DEMetro_Z 0.99 -3.421 0.00571 -0.988
HMC_vs_Metro 0.0 -4.757 0.000593 -1.373
HMC_vs_Metro 0.3 -2.282 0.0434 -0.659
HMC_vs_Metro 0.5 -0.510 0.62 -0.147
HMC_vs_Metro 0.9 -3.971 0.00219 -1.146
HMC_vs_Metro 0.99 -7.617 1.04e-05 -2.199
HMC_vs_SMC 0.0 0.897 0.389 0.259
HMC_vs_SMC 0.3 0.678 0.512 0.196
HMC_vs_SMC 0.5 0.696 0.501 0.201
HMC_vs_SMC 0.9 6.317 5.7e-05 1.823
HMC_vs_SMC 0.99 0.644 0.533 0.186
Metro_vs_SMC 0.0 5.488 0.00019 1.584
Metro_vs_SMC 0.3 2.496 0.0297 0.720
Metro_vs_SMC 0.5 1.701 0.117 0.491
Metro_vs_SMC 0.9 6.144 7.27e-05 1.774
Metro_vs_SMC 0.99 6.588 3.93e-05 1.902
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.138 0.122 0.038 0.430
HMC 0.3 0.129 0.119 0.020 0.510
HMC 0.5 0.170 0.103 0.025 2.603
HMC 0.9 0.182 0.099 0.027 3.074
HMC 0.99 0.172 0.111 0.074 0.824
SMC 0.0 0.129 0.122 0.038 0.180
SMC 0.3 0.118 0.119 0.020 -0.035
SMC 0.5 0.137 0.103 0.025 1.333
SMC 0.9 0.103 0.099 0.027 0.142
SMC 0.99 0.147 0.111 0.074 0.487
Metro 0.0 0.194 0.122 0.038 1.903
Metro 0.3 0.262 0.119 0.020 7.315
Metro 0.5 0.188 0.103 0.025 3.304
Metro 0.9 0.365 0.099 0.027 9.905
Metro 0.99 0.749 0.111 0.074 8.560
DEMetro_Z 0.0 0.277 0.122 0.038 4.109
DEMetro_Z 0.3 0.272 0.119 0.020 7.812
DEMetro_Z 0.5 0.235 0.103 0.025 5.163
DEMetro_Z 0.9 0.265 0.099 0.027 6.197
DEMetro_Z 0.99 0.259 0.111 0.074 1.984
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 2.221 0.0373 0.998
HMC 0.3 2.019 0.0635 1.756
HMC 0.5 3.606 0.00184 1.854
HMC 0.9 2.895 0.00998 1.724
HMC 0.99 4.503 0.000473 3.570
SMC 0.0 0.043 0.966 0.019
SMC 0.3 1.522 0.146 0.908
SMC 0.5 2.324 0.0347 1.713
SMC 0.9 -0.126 0.901 -0.049
SMC 0.99 2.757 0.0163 2.704
Metro 0.0 4.289 0.000864 4.157
Metro 0.3 6.227 3.05e-05 6.165
Metro 0.5 6.873 8.78e-06 6.023
Metro 0.9 4.737 0.000561 10.792
Metro 0.99 5.931 9.78e-05 55.272
DEMetro_Z 0.0 3.486 0.00483 7.361
DEMetro_Z 0.3 6.091 5.26e-05 8.117
DEMetro_Z 0.5 8.487 2.26e-07 5.437
DEMetro_Z 0.9 4.978 0.000152 3.445
DEMetro_Z 0.99 6.175 4.35e-05 7.679
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 3.322 0.00681 0.959
DEMetro_Z_vs_SMC 0.3 5.503 0.000185 1.589
DEMetro_Z_vs_SMC 0.5 3.793 0.00298 1.095
DEMetro_Z_vs_SMC 0.9 5.036 0.00038 1.454
DEMetro_Z_vs_SMC 0.99 3.331 0.0067 0.962
HMC_vs_Metro 0.0 -3.330 0.00671 -0.961
HMC_vs_Metro 0.3 -3.105 0.01 -0.896
HMC_vs_Metro 0.5 -4.864 0.0005 -1.404
HMC_vs_Metro 0.9 -3.823 0.00283 -1.104
HMC_vs_Metro 0.99 -5.774 0.000124 -1.667
Metro_vs_DEMetro_Z 0.0 -1.361 0.201 -0.393
Metro_vs_DEMetro_Z 0.3 -1.025 0.327 -0.296
Metro_vs_DEMetro_Z 0.5 0.514 0.618 0.148
Metro_vs_DEMetro_Z 0.9 3.145 0.00932 0.908
Metro_vs_DEMetro_Z 0.99 5.091 0.000349 1.470
HMC_vs_SMC 0.0 2.575 0.0258 0.743
HMC_vs_SMC 0.3 0.768 0.459 0.222
HMC_vs_SMC 0.5 0.217 0.832 0.063
HMC_vs_SMC 0.9 2.610 0.0243 0.753
HMC_vs_SMC 0.99 0.672 0.515 0.194
Metro_vs_SMC 0.0 4.613 0.000749 1.332
Metro_vs_SMC 0.3 4.159 0.00159 1.201
Metro_vs_SMC 0.5 3.688 0.00358 1.065
Metro_vs_SMC 0.9 4.597 0.000769 1.327
Metro_vs_SMC 0.99 5.517 0.000181 1.593
HMC_vs_DEMetro_Z 0.0 -3.053 0.011 -0.881
HMC_vs_DEMetro_Z 0.3 -3.601 0.00416 -1.040
HMC_vs_DEMetro_Z 0.5 -6.097 7.77e-05 -1.760
HMC_vs_DEMetro_Z 0.9 -2.222 0.0482 -0.641
HMC_vs_DEMetro_Z 0.99 -3.374 0.00621 -0.974
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.019 0.014 0.004 0.998
HMC 0.3 0.019 0.014 0.003 1.756
HMC 0.5 0.020 0.014 0.004 1.854
HMC 0.9 0.024 0.015 0.005 1.724
HMC 0.99 0.030 0.015 0.004 3.570
SMC 0.0 0.015 0.014 0.004 0.019
SMC 0.3 0.017 0.014 0.003 0.908
SMC 0.5 0.020 0.014 0.004 1.713
SMC 0.9 0.015 0.015 0.005 -0.049
SMC 0.99 0.027 0.015 0.004 2.704
Metro 0.0 0.033 0.014 0.004 4.157
Metro 0.3 0.033 0.014 0.003 6.165
Metro 0.5 0.035 0.014 0.004 6.023
Metro 0.9 0.072 0.015 0.005 10.792
Metro 0.99 0.254 0.015 0.004 55.272
DEMetro_Z 0.0 0.047 0.014 0.004 7.361
DEMetro_Z 0.3 0.038 0.014 0.003 8.117
DEMetro_Z 0.5 0.033 0.014 0.004 5.437
DEMetro_Z 0.9 0.033 0.015 0.005 3.445
DEMetro_Z 0.99 0.048 0.015 0.004 7.679
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
0.0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.9 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.99 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0.0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.9 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.99 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.99
Chain
0.0
0.3
0.5
0.9
0.99

Vary_Correlation_with_high_Multimodality (Mixture, correlation, 12 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 4.017 0.00201 30.053
HMC 0.3 4.600 0.000759 34.242
HMC 0.5 2.200 0.0501 24.498
HMC 0.9 4.145 0.00162 27.478
HMC 0.99 2.899 0.0145 37.866
SMC 0.0 0.159 0.875 0.069
SMC 0.3 0.942 0.357 0.450
SMC 0.5 0.448 0.66 0.152
SMC 0.9 0.978 0.34 0.463
SMC 0.99 0.554 0.586 0.289
Metro 0.0 3.453 0.00538 26.777
Metro 0.3 4.008 0.00204 26.862
Metro 0.5 2.850 0.0158 23.856
Metro 0.9 4.367 0.00111 28.000
Metro 0.99 3.660 0.00374 44.643
DEMetro_Z 0.0 4.528 0.000855 37.040
DEMetro_Z 0.3 4.657 0.000687 25.453
DEMetro_Z 0.5 3.700 0.00349 44.902
DEMetro_Z 0.9 4.080 0.00181 27.284
DEMetro_Z 0.99 3.940 0.00231 53.457
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -0.558 0.588 -0.161
HMC_vs_DEMetro_Z 0.3 0.863 0.407 0.249
HMC_vs_DEMetro_Z 0.5 -1.405 0.188 -0.406
HMC_vs_DEMetro_Z 0.9 0.021 0.984 0.006
HMC_vs_DEMetro_Z 0.99 -0.881 0.397 -0.254
Metro_vs_SMC 0.0 3.464 0.0053 1.000
Metro_vs_SMC 0.3 4.052 0.00191 1.170
Metro_vs_SMC 0.5 2.863 0.0154 0.826
Metro_vs_SMC 0.9 4.161 0.00159 1.201
Metro_vs_SMC 0.99 3.563 0.00445 1.028
Metro_vs_DEMetro_Z 0.0 -0.875 0.4 -0.252
Metro_vs_DEMetro_Z 0.3 0.144 0.888 0.042
Metro_vs_DEMetro_Z 0.5 -1.323 0.213 -0.382
Metro_vs_DEMetro_Z 0.9 0.081 0.937 0.023
Metro_vs_DEMetro_Z 0.99 -0.584 0.571 -0.168
HMC_vs_Metro 0.0 0.940 0.368 0.271
HMC_vs_Metro 0.3 0.954 0.361 0.275
HMC_vs_Metro 0.5 0.041 0.968 0.012
HMC_vs_Metro 0.9 -0.083 0.936 -0.024
HMC_vs_Metro 0.99 -0.335 0.744 -0.097
HMC_vs_SMC 0.0 4.035 0.00197 1.165
HMC_vs_SMC 0.3 4.675 0.000677 1.350
HMC_vs_SMC 0.5 2.170 0.0528 0.626
HMC_vs_SMC 0.9 4.011 0.00205 1.158
HMC_vs_SMC 0.99 2.895 0.0146 0.836
DEMetro_Z_vs_SMC 0.0 4.494 0.000911 1.297
DEMetro_Z_vs_SMC 0.3 4.575 0.000796 1.321
DEMetro_Z_vs_SMC 0.5 3.667 0.00371 1.059
DEMetro_Z_vs_SMC 0.9 4.011 0.00205 1.158
DEMetro_Z_vs_SMC 0.99 3.929 0.00235 1.134
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 1.743 0.092 0.055 30.053
HMC 0.3 2.090 0.101 0.058 34.242
HMC 0.5 1.008 0.046 0.039 24.498
HMC 0.9 1.743 0.074 0.061 27.478
HMC 0.99 1.545 0.079 0.039 37.866
SMC 0.0 0.096 0.092 0.055 0.069
SMC 0.3 0.127 0.101 0.058 0.450
SMC 0.5 0.052 0.046 0.039 0.152
SMC 0.9 0.102 0.074 0.061 0.463
SMC 0.99 0.090 0.079 0.039 0.289
Metro 0.0 1.563 0.092 0.055 26.777
Metro 0.3 1.661 0.101 0.058 26.862
Metro 0.5 0.983 0.046 0.039 23.856
Metro 0.9 1.774 0.074 0.061 28.000
Metro 0.99 1.808 0.079 0.039 44.643
DEMetro_Z 0.0 2.126 0.092 0.055 37.040
DEMetro_Z 0.3 1.579 0.101 0.058 25.453
DEMetro_Z 0.5 1.810 0.046 0.039 44.902
DEMetro_Z 0.9 1.731 0.074 0.061 27.284
DEMetro_Z 0.99 2.149 0.079 0.039 53.457
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 2.883 0.0149 46.926
HMC 0.3 3.141 0.00939 66.429
HMC 0.5 1.737 0.11 47.528
HMC 0.9 2.942 0.0134 72.980
HMC 0.99 2.314 0.041 60.419
SMC 0.0 0.408 0.688 0.169
SMC 0.3 0.189 0.852 0.074
SMC 0.5 1.148 0.27 0.969
SMC 0.9 1.006 0.328 0.603
SMC 0.99 -1.489 0.151 -0.597
Metro 0.0 2.571 0.026 43.000
Metro 0.3 2.769 0.0182 46.661
Metro 0.5 3.024 0.0116 34.131
Metro 0.9 3.042 0.0112 73.981
Metro 0.99 3.077 0.0105 74.455
DEMetro_Z 0.0 2.920 0.0139 66.382
DEMetro_Z 0.3 2.454 0.032 37.863
DEMetro_Z 0.5 2.872 0.0152 92.045
DEMetro_Z 0.9 2.952 0.0132 72.746
DEMetro_Z 0.99 3.002 0.012 86.033
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 2.851 0.0158 0.823
HMC_vs_SMC 0.3 3.137 0.00947 0.905
HMC_vs_SMC 0.5 1.688 0.119 0.487
HMC_vs_SMC 0.9 2.894 0.0146 0.835
HMC_vs_SMC 0.99 2.358 0.038 0.681
Metro_vs_DEMetro_Z 0.0 -0.817 0.431 -0.236
Metro_vs_DEMetro_Z 0.3 0.366 0.722 0.106
Metro_vs_DEMetro_Z 0.5 -1.610 0.136 -0.465
Metro_vs_DEMetro_Z 0.9 0.033 0.974 0.010
Metro_vs_DEMetro_Z 0.99 -0.484 0.638 -0.140
HMC_vs_Metro 0.0 1.016 0.331 0.293
HMC_vs_Metro 0.3 1.241 0.24 0.358
HMC_vs_Metro 0.5 0.413 0.688 0.119
HMC_vs_Metro 0.9 -0.073 0.943 -0.021
HMC_vs_Metro 0.99 -0.352 0.731 -0.102
HMC_vs_DEMetro_Z 0.0 -0.665 0.519 -0.192
HMC_vs_DEMetro_Z 0.3 0.996 0.341 0.287
HMC_vs_DEMetro_Z 0.5 -1.042 0.32 -0.301
HMC_vs_DEMetro_Z 0.9 0.006 0.995 0.002
HMC_vs_DEMetro_Z 0.99 -0.731 0.48 -0.211
Metro_vs_SMC 0.0 2.543 0.0273 0.734
Metro_vs_SMC 0.3 2.779 0.018 0.802
Metro_vs_SMC 0.5 2.878 0.015 0.831
Metro_vs_SMC 0.9 3.005 0.012 0.868
Metro_vs_SMC 0.99 3.094 0.0102 0.893
DEMetro_Z_vs_SMC 0.0 2.917 0.014 0.842
DEMetro_Z_vs_SMC 0.3 2.428 0.0335 0.701
DEMetro_Z_vs_SMC 0.5 2.817 0.0167 0.813
DEMetro_Z_vs_SMC 0.9 2.930 0.0137 0.846
DEMetro_Z_vs_SMC 0.99 3.030 0.0114 0.875
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 6.875 0.187 0.143 46.926
HMC 0.3 9.308 0.190 0.137 66.429
HMC 0.5 4.457 0.144 0.091 47.528
HMC 0.9 6.925 0.111 0.093 72.980
HMC 0.99 7.546 0.199 0.122 60.419
SMC 0.0 0.211 0.187 0.143 0.169
SMC 0.3 0.200 0.190 0.137 0.074
SMC 0.5 0.232 0.144 0.091 0.969
SMC 0.9 0.167 0.111 0.093 0.603
SMC 0.99 0.126 0.199 0.122 -0.597
Metro 0.0 6.316 0.187 0.143 43.000
Metro 0.3 6.595 0.190 0.137 46.661
Metro 0.5 3.241 0.144 0.091 34.131
Metro 0.9 7.019 0.111 0.093 73.981
Metro 0.99 9.252 0.199 0.122 74.455
DEMetro_Z 0.0 9.649 0.187 0.143 66.382
DEMetro_Z 0.3 5.387 0.190 0.137 37.863
DEMetro_Z 0.5 8.498 0.144 0.091 92.045
DEMetro_Z 0.9 6.903 0.111 0.093 72.746
DEMetro_Z 0.99 10.660 0.199 0.122 86.033
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 3.830 0.00278 34.209
HMC 0.3 4.709 0.000635 33.350
HMC 0.5 2.109 0.0587 27.856
HMC 0.9 4.103 0.00174 28.141
HMC 0.99 2.884 0.0148 39.222
SMC 0.0 -0.016 0.988 -0.007
SMC 0.3 0.978 0.339 0.457
SMC 0.5 0.208 0.838 0.074
SMC 0.9 0.866 0.396 0.399
SMC 0.99 0.279 0.783 0.141
Metro 0.0 3.534 0.00467 31.336
Metro 0.3 3.820 0.00283 26.251
Metro 0.5 2.884 0.0148 26.805
Metro 0.9 4.613 0.000741 29.498
Metro 0.99 4.014 0.00203 48.651
DEMetro_Z 0.0 4.442 0.000987 44.517
DEMetro_Z 0.3 4.425 0.00101 26.599
DEMetro_Z 0.5 3.628 0.00396 51.562
DEMetro_Z 0.9 4.267 0.00132 27.851
DEMetro_Z 0.99 4.012 0.00204 55.657
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -0.932 0.372 -0.269
Metro_vs_DEMetro_Z 0.3 -0.035 0.973 -0.010
Metro_vs_DEMetro_Z 0.5 -1.327 0.211 -0.383
Metro_vs_DEMetro_Z 0.9 0.186 0.856 0.054
Metro_vs_DEMetro_Z 0.99 -0.482 0.639 -0.139
DEMetro_Z_vs_SMC 0.0 4.403 0.00106 1.271
DEMetro_Z_vs_SMC 0.3 4.324 0.00121 1.248
DEMetro_Z_vs_SMC 0.5 3.600 0.00417 1.039
DEMetro_Z_vs_SMC 0.9 4.198 0.00149 1.212
DEMetro_Z_vs_SMC 0.99 4.017 0.00203 1.160
HMC_vs_DEMetro_Z 0.0 -0.697 0.5 -0.201
HMC_vs_DEMetro_Z 0.3 0.648 0.53 0.187
HMC_vs_DEMetro_Z 0.5 -1.389 0.192 -0.401
HMC_vs_DEMetro_Z 0.9 0.030 0.976 0.009
HMC_vs_DEMetro_Z 0.99 -0.904 0.385 -0.261
HMC_vs_Metro 0.0 0.709 0.493 0.205
HMC_vs_Metro 0.3 0.916 0.379 0.264
HMC_vs_Metro 0.5 0.058 0.955 0.017
HMC_vs_Metro 0.9 -0.198 0.847 -0.057
HMC_vs_Metro 0.99 -0.465 0.651 -0.134
HMC_vs_SMC 0.0 3.842 0.00274 1.109
HMC_vs_SMC 0.3 4.792 0.000561 1.383
HMC_vs_SMC 0.5 2.090 0.0606 0.603
HMC_vs_SMC 0.9 3.991 0.00212 1.152
HMC_vs_SMC 0.99 2.898 0.0145 0.837
Metro_vs_SMC 0.0 3.548 0.00457 1.024
Metro_vs_SMC 0.3 3.878 0.00257 1.119
Metro_vs_SMC 0.5 2.888 0.0148 0.834
Metro_vs_SMC 0.9 4.426 0.00102 1.278
Metro_vs_SMC 0.99 3.925 0.00237 1.133
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 1.537 0.101 0.042 34.209
HMC 0.3 1.810 0.108 0.051 33.350
HMC 0.5 0.913 0.065 0.030 27.856
HMC 0.9 1.547 0.084 0.052 28.141
HMC 0.99 1.413 0.092 0.034 39.222
SMC 0.0 0.100 0.101 0.042 -0.007
SMC 0.3 0.131 0.108 0.051 0.457
SMC 0.5 0.067 0.065 0.030 0.074
SMC 0.9 0.104 0.084 0.052 0.399
SMC 0.99 0.097 0.092 0.034 0.141
Metro 0.0 1.416 0.101 0.042 31.336
Metro 0.3 1.448 0.108 0.051 26.251
Metro 0.5 0.881 0.065 0.030 26.805
Metro 0.9 1.618 0.084 0.052 29.498
Metro 0.99 1.730 0.092 0.034 48.651
DEMetro_Z 0.0 1.969 0.101 0.042 44.517
DEMetro_Z 0.3 1.466 0.108 0.051 26.599
DEMetro_Z 0.5 1.636 0.065 0.030 51.562
DEMetro_Z 0.9 1.532 0.084 0.052 27.851
DEMetro_Z 0.99 1.966 0.092 0.034 55.657
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 4.047 0.00191 31.850
HMC 0.3 4.711 0.000634 38.778
HMC 0.5 2.227 0.0478 31.111
HMC 0.9 4.129 0.00166 28.430
HMC 0.99 2.969 0.0128 47.993
SMC 0.0 -0.215 0.832 -0.088
SMC 0.3 1.120 0.276 0.529
SMC 0.5 0.494 0.627 0.170
SMC 0.9 0.521 0.608 0.221
SMC 0.99 0.551 0.588 0.333
Metro 0.0 3.488 0.00506 28.224
Metro 0.3 4.055 0.00189 30.411
Metro 0.5 2.854 0.0157 30.730
Metro 0.9 4.425 0.00101 28.553
Metro 0.99 3.844 0.00273 59.608
DEMetro_Z 0.0 4.696 0.00065 38.847
DEMetro_Z 0.3 5.006 0.000393 29.295
DEMetro_Z 0.5 3.721 0.00337 56.487
DEMetro_Z 0.9 4.168 0.00155 27.674
DEMetro_Z 0.99 4.015 0.00203 66.484
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 4.674 0.000678 1.349
DEMetro_Z_vs_SMC 0.3 4.895 0.000476 1.413
DEMetro_Z_vs_SMC 0.5 3.694 0.00354 1.066
DEMetro_Z_vs_SMC 0.9 4.144 0.00163 1.196
DEMetro_Z_vs_SMC 0.99 4.003 0.00207 1.156
HMC_vs_Metro 0.0 0.924 0.375 0.267
HMC_vs_Metro 0.3 0.944 0.365 0.273
HMC_vs_Metro 0.5 0.019 0.985 0.006
HMC_vs_Metro 0.9 -0.019 0.985 -0.005
HMC_vs_Metro 0.99 -0.453 0.659 -0.131
Metro_vs_DEMetro_Z 0.0 -0.879 0.398 -0.254
Metro_vs_DEMetro_Z 0.3 0.104 0.919 0.030
Metro_vs_DEMetro_Z 0.5 -1.280 0.227 -0.369
Metro_vs_DEMetro_Z 0.9 0.099 0.923 0.029
Metro_vs_DEMetro_Z 0.99 -0.353 0.731 -0.102
HMC_vs_SMC 0.0 4.083 0.00181 1.179
HMC_vs_SMC 0.3 4.776 0.000575 1.379
HMC_vs_SMC 0.5 2.196 0.0504 0.634
HMC_vs_SMC 0.9 4.048 0.00192 1.169
HMC_vs_SMC 0.99 2.961 0.0129 0.855
Metro_vs_SMC 0.0 3.521 0.00479 1.016
Metro_vs_SMC 0.3 4.075 0.00184 1.176
Metro_vs_SMC 0.5 2.853 0.0157 0.824
Metro_vs_SMC 0.9 4.285 0.00129 1.237
Metro_vs_SMC 0.99 3.741 0.00326 1.080
HMC_vs_DEMetro_Z 0.0 -0.538 0.601 -0.155
HMC_vs_DEMetro_Z 0.3 0.857 0.41 0.247
HMC_vs_DEMetro_Z 0.5 -1.443 0.177 -0.416
HMC_vs_DEMetro_Z 0.9 0.080 0.938 0.023
HMC_vs_DEMetro_Z 0.99 -0.848 0.415 -0.245
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.246 0.013 0.007 31.850
HMC 0.3 0.293 0.014 0.007 38.778
HMC 0.5 0.141 0.007 0.004 31.111
HMC 0.9 0.251 0.010 0.008 28.430
HMC 0.99 0.218 0.011 0.004 47.993
SMC 0.0 0.013 0.013 0.007 -0.088
SMC 0.3 0.017 0.014 0.007 0.529
SMC 0.5 0.008 0.007 0.004 0.170
SMC 0.9 0.012 0.010 0.008 0.221
SMC 0.99 0.012 0.011 0.004 0.333
Metro 0.0 0.220 0.013 0.007 28.224
Metro 0.3 0.233 0.014 0.007 30.411
Metro 0.5 0.139 0.007 0.004 30.730
Metro 0.9 0.252 0.010 0.008 28.553
Metro 0.99 0.269 0.011 0.004 59.608
DEMetro_Z 0.0 0.297 0.013 0.007 38.847
DEMetro_Z 0.3 0.225 0.014 0.007 29.295
DEMetro_Z 0.5 0.250 0.007 0.004 56.487
DEMetro_Z 0.9 0.245 0.010 0.008 27.674
DEMetro_Z 0.99 0.298 0.011 0.004 66.484
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 172.154 6.01e-34 82.016
HMC 0.3 141.550 1.91e-29 77.236
HMC 0.5 207.636 4.2e-32 115.379
HMC 0.9 162.269 3.94e-34 74.489
HMC 0.99 179.000 5.49e-28 116.364
SMC 0.0 0.188 0.853 0.082
SMC 0.3 0.356 0.726 0.166
SMC 0.5 1.638 0.117 0.776
SMC 0.9 1.219 0.236 0.484
SMC 0.99 0.424 0.676 0.221
Metro 0.0 167.950 3.53e-33 82.138
Metro 0.3 147.417 2e-30 77.908
Metro 0.5 188.391 2.1e-29 115.277
Metro 0.9 137.567 2.99e-29 74.934
Metro 0.99 54.838 3.34e-15 114.334
DEMetro_Z 0.0 8.442 3.84e-06 69.852
DEMetro_Z 0.3 5.246 0.000273 53.742
DEMetro_Z 0.5 8.651 3.05e-06 99.645
DEMetro_Z 0.9 13.002 4.77e-08 69.092
DEMetro_Z 0.99 182.558 2.23e-28 116.874
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 1.467 0.17 0.424
HMC_vs_DEMetro_Z 0.3 2.361 0.0377 0.682
HMC_vs_DEMetro_Z 0.5 1.391 0.192 0.402
HMC_vs_DEMetro_Z 0.9 1.016 0.331 0.293
HMC_vs_DEMetro_Z 0.99 -0.597 0.563 -0.172
Metro_vs_SMC 0.0 153.819 1.1e-19 44.404
Metro_vs_SMC 0.3 143.411 2.37e-19 41.399
Metro_vs_SMC 0.5 138.373 3.52e-19 39.945
Metro_vs_SMC 0.9 155.230 9.94e-20 44.811
Metro_vs_SMC 0.99 56.387 6.74e-15 16.278
Metro_vs_DEMetro_Z 0.0 1.472 0.169 0.425
Metro_vs_DEMetro_Z 0.3 2.307 0.0415 0.666
Metro_vs_DEMetro_Z 0.5 1.388 0.193 0.401
Metro_vs_DEMetro_Z 0.9 1.098 0.296 0.317
Metro_vs_DEMetro_Z 0.99 -1.496 0.163 -0.432
HMC_vs_Metro 0.0 -0.762 0.462 -0.220
HMC_vs_Metro 0.3 -0.900 0.387 -0.260
HMC_vs_Metro 0.5 0.400 0.697 0.116
HMC_vs_Metro 0.9 -0.811 0.435 -0.234
HMC_vs_Metro 0.99 1.061 0.311 0.306
HMC_vs_SMC 0.0 154.356 1.06e-19 44.559
HMC_vs_SMC 0.3 104.587 7.63e-18 30.192
HMC_vs_SMC 0.5 147.331 1.76e-19 42.531
HMC_vs_SMC 0.9 156.112 9.34e-20 45.066
HMC_vs_SMC 0.99 167.606 4.28e-20 48.384
DEMetro_Z_vs_SMC 0.0 8.419 4.01e-06 2.430
DEMetro_Z_vs_SMC 0.3 5.218 0.000287 1.506
DEMetro_Z_vs_SMC 0.5 8.420 4e-06 2.431
DEMetro_Z_vs_SMC 0.9 12.927 5.39e-08 3.732
DEMetro_Z_vs_SMC 0.99 153.290 1.14e-19 44.251
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 4.596 0.092 0.055 82.016
HMC 0.3 4.587 0.101 0.058 77.236
HMC 0.5 4.577 0.046 0.039 115.379
HMC 0.9 4.598 0.074 0.061 74.489
HMC 0.99 4.585 0.079 0.039 116.364
SMC 0.0 0.097 0.092 0.055 0.082
SMC 0.3 0.111 0.101 0.058 0.166
SMC 0.5 0.077 0.046 0.039 0.776
SMC 0.9 0.103 0.074 0.061 0.484
SMC 0.99 0.087 0.079 0.039 0.221
Metro 0.0 4.603 0.092 0.055 82.138
Metro 0.3 4.626 0.101 0.058 77.908
Metro 0.5 4.573 0.046 0.039 115.277
Metro 0.9 4.625 0.074 0.061 74.934
Metro 0.99 4.507 0.079 0.039 114.334
DEMetro_Z 0.0 3.928 0.092 0.055 69.852
DEMetro_Z 0.3 3.222 0.101 0.058 53.742
DEMetro_Z 0.5 3.959 0.046 0.039 99.645
DEMetro_Z 0.9 4.270 0.074 0.061 69.092
DEMetro_Z 0.99 4.605 0.079 0.039 116.874
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 460.440 5.08e-44 208.235
HMC 0.3 544.910 8.97e-47 215.797
HMC 0.5 533.268 6.41e-37 327.448
HMC 0.9 563.109 1.87e-39 318.667
HMC 0.99 560.081 1.39e-46 244.148
SMC 0.0 -0.199 0.844 -0.071
SMC 0.3 0.880 0.389 0.314
SMC 0.5 0.695 0.497 0.447
SMC 0.9 2.578 0.0194 1.528
SMC 0.99 -1.636 0.118 -0.567
Metro 0.0 451.464 2.22e-43 208.230
Metro 0.3 514.118 2.94e-46 215.852
Metro 0.5 492.084 1.45e-34 327.549
Metro 0.9 622.830 2.9e-43 318.635
Metro 0.99 354.135 1.38e-31 245.318
DEMetro_Z 0.0 7.416 1.33e-05 173.648
DEMetro_Z 0.3 4.769 0.000581 144.556
DEMetro_Z 0.5 7.466 1.25e-05 273.016
DEMetro_Z 0.9 11.133 2.5e-07 292.740
DEMetro_Z 0.99 570.382 4.84e-47 244.033
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 437.137 1.13e-24 126.191
HMC_vs_SMC 0.3 582.634 4.78e-26 168.192
HMC_vs_SMC 0.5 444.121 9.47e-25 128.207
HMC_vs_SMC 0.9 473.474 4.68e-25 136.680
HMC_vs_SMC 0.99 549.683 9.07e-26 158.680
Metro_vs_DEMetro_Z 0.0 1.488 0.165 0.430
Metro_vs_DEMetro_Z 0.3 2.348 0.0386 0.678
Metro_vs_DEMetro_Z 0.5 1.481 0.167 0.427
Metro_vs_DEMetro_Z 0.9 0.986 0.345 0.285
Metro_vs_DEMetro_Z 0.99 2.166 0.0531 0.625
HMC_vs_Metro 0.0 0.044 0.966 0.013
HMC_vs_Metro 0.3 -0.713 0.491 -0.206
HMC_vs_Metro 0.5 -0.544 0.597 -0.157
HMC_vs_Metro 0.9 0.113 0.912 0.033
HMC_vs_Metro 0.99 -2.027 0.0676 -0.585
HMC_vs_DEMetro_Z 0.0 1.488 0.165 0.430
HMC_vs_DEMetro_Z 0.3 2.350 0.0385 0.678
HMC_vs_DEMetro_Z 0.5 1.479 0.167 0.427
HMC_vs_DEMetro_Z 0.9 0.990 0.344 0.286
HMC_vs_DEMetro_Z 0.99 0.854 0.411 0.247
Metro_vs_SMC 0.0 423.613 1.59e-24 122.287
Metro_vs_SMC 0.3 553.142 8.47e-26 159.678
Metro_vs_SMC 0.5 421.813 1.67e-24 121.767
Metro_vs_SMC 0.9 457.108 6.9e-25 131.956
Metro_vs_SMC 0.99 403.537 2.72e-24 116.491
DEMetro_Z_vs_SMC 0.0 7.367 1.42e-05 2.127
DEMetro_Z_vs_SMC 0.3 4.769 0.000582 1.377
DEMetro_Z_vs_SMC 0.5 7.421 1.32e-05 2.142
DEMetro_Z_vs_SMC 0.9 11.111 2.55e-07 3.208
DEMetro_Z_vs_SMC 0.99 555.370 8.1e-26 160.321
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 29.869 0.187 0.143 208.235
HMC 0.3 29.810 0.190 0.137 215.797
HMC 0.5 29.864 0.144 0.091 327.448
HMC 0.9 29.866 0.111 0.093 318.667
HMC 0.99 29.886 0.199 0.122 244.148
SMC 0.0 0.176 0.187 0.143 -0.071
SMC 0.3 0.233 0.190 0.137 0.314
SMC 0.5 0.184 0.144 0.091 0.447
SMC 0.9 0.254 0.111 0.093 1.528
SMC 0.99 0.130 0.199 0.122 -0.567
Metro 0.0 29.868 0.187 0.143 208.230
Metro 0.3 29.818 0.190 0.137 215.852
Metro 0.5 29.873 0.144 0.091 327.549
Metro 0.9 29.863 0.111 0.093 318.635
Metro 0.99 30.028 0.199 0.122 245.318
DEMetro_Z 0.0 24.939 0.187 0.143 173.648
DEMetro_Z 0.3 20.032 0.190 0.137 144.556
DEMetro_Z 0.5 24.923 0.144 0.091 273.016
DEMetro_Z 0.9 27.445 0.111 0.093 292.740
DEMetro_Z 0.99 29.872 0.199 0.122 244.033
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 53.525 2.99e-15 94.972
HMC 0.3 55.130 9.11e-16 77.645
HMC 0.5 55.015 4.08e-15 130.828
HMC 0.9 41.815 5.52e-14 76.214
HMC 0.99 55.693 3.11e-15 122.474
SMC 0.0 0.236 0.816 0.109
SMC 0.3 0.524 0.606 0.249
SMC 0.5 1.699 0.105 0.835
SMC 0.9 1.290 0.211 0.531
SMC 0.99 0.153 0.88 0.072
Metro 0.0 53.249 3.46e-15 97.462
Metro 0.3 57.314 5.19e-16 79.086
Metro 0.5 45.481 4.42e-14 132.220
Metro 0.9 50.878 3.65e-15 79.824
Metro 0.99 44.584 5.22e-14 122.527
DEMetro_Z 0.0 8.388 4.1e-06 80.001
DEMetro_Z 0.3 5.249 0.000271 52.526
DEMetro_Z 0.5 8.417 3.99e-06 115.485
DEMetro_Z 0.9 12.665 6.32e-08 71.226
DEMetro_Z 0.99 66.802 2.67e-16 124.541
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 1.759 0.106 0.508
Metro_vs_DEMetro_Z 0.3 2.563 0.0264 0.740
Metro_vs_DEMetro_Z 0.5 1.292 0.223 0.373
Metro_vs_DEMetro_Z 0.9 1.856 0.0904 0.536
Metro_vs_DEMetro_Z 0.99 -0.626 0.544 -0.181
DEMetro_Z_vs_SMC 0.0 8.383 4.18e-06 2.420
DEMetro_Z_vs_SMC 0.3 5.221 0.000285 1.507
DEMetro_Z_vs_SMC 0.5 8.189 5.23e-06 2.364
DEMetro_Z_vs_SMC 0.9 12.689 6.54e-08 3.663
DEMetro_Z_vs_SMC 0.99 75.423 2.77e-16 21.773
HMC_vs_DEMetro_Z 0.0 1.766 0.105 0.510
HMC_vs_DEMetro_Z 0.3 2.574 0.0259 0.743
HMC_vs_DEMetro_Z 0.5 1.196 0.257 0.345
HMC_vs_DEMetro_Z 0.9 0.910 0.382 0.263
HMC_vs_DEMetro_Z 0.99 -0.737 0.476 -0.213
HMC_vs_Metro 0.0 -0.966 0.355 -0.279
HMC_vs_Metro 0.3 -0.948 0.363 -0.274
HMC_vs_Metro 0.5 -0.397 0.699 -0.114
HMC_vs_Metro 0.9 -1.472 0.169 -0.425
HMC_vs_Metro 0.99 -0.015 0.988 -0.004
HMC_vs_SMC 0.0 52.832 1.38e-14 15.251
HMC_vs_SMC 0.3 51.770 1.72e-14 14.945
HMC_vs_SMC 0.5 49.518 2.8e-14 14.295
HMC_vs_SMC 0.9 40.670 2.41e-13 11.740
HMC_vs_SMC 0.99 54.724 9.35e-15 15.797
Metro_vs_SMC 0.0 55.221 8.47e-15 15.941
Metro_vs_SMC 0.3 55.263 8.4e-15 15.953
Metro_vs_SMC 0.5 41.852 1.76e-13 12.082
Metro_vs_SMC 0.9 53.878 1.11e-14 15.553
Metro_vs_SMC 0.99 44.366 9.32e-14 12.807
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 4.087 0.101 0.042 94.972
HMC 0.3 4.072 0.108 0.051 77.645
HMC 0.5 4.051 0.065 0.030 130.828
HMC 0.9 4.047 0.084 0.052 76.214
HMC 0.99 4.217 0.092 0.034 122.474
SMC 0.0 0.105 0.101 0.042 0.109
SMC 0.3 0.120 0.108 0.051 0.249
SMC 0.5 0.090 0.065 0.030 0.835
SMC 0.9 0.111 0.084 0.052 0.531
SMC 0.99 0.094 0.092 0.034 0.072
Metro 0.0 4.192 0.101 0.042 97.462
Metro 0.3 4.146 0.108 0.051 79.086
Metro 0.5 4.093 0.065 0.030 132.220
Metro 0.9 4.235 0.084 0.052 79.824
Metro 0.99 4.219 0.092 0.034 122.527
DEMetro_Z 0.0 3.459 0.101 0.042 80.001
DEMetro_Z 0.3 2.790 0.108 0.051 52.526
DEMetro_Z 0.5 3.583 0.065 0.030 115.485
DEMetro_Z 0.9 3.787 0.084 0.052 71.226
DEMetro_Z 0.99 4.287 0.092 0.034 124.541
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 116.322 6.56e-24 82.057
HMC 0.3 116.564 1.27e-23 84.366
HMC 0.5 134.514 1.32e-21 139.327
HMC 0.9 110.426 1.57e-24 72.216
HMC 0.99 95.055 1.85e-18 141.698
SMC 0.0 0.207 0.838 0.096
SMC 0.3 0.443 0.662 0.198
SMC 0.5 1.953 0.066 1.059
SMC 0.9 1.004 0.327 0.371
SMC 0.99 0.373 0.714 0.214
Metro 0.0 115.377 1.04e-23 82.409
Metro 0.3 96.318 1.05e-20 84.597
Metro 0.5 98.817 8.86e-19 139.932
Metro 0.9 95.881 6.58e-22 72.508
Metro 0.99 65.647 5.14e-16 149.623
DEMetro_Z 0.0 8.481 3.67e-06 70.982
DEMetro_Z 0.3 5.433 0.000205 58.667
DEMetro_Z 0.5 8.740 2.77e-06 121.358
DEMetro_Z 0.9 13.132 4.27e-08 66.776
DEMetro_Z 0.99 95.901 1.72e-18 143.740
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 8.494 3.68e-06 2.452
DEMetro_Z_vs_SMC 0.3 5.411 0.000213 1.562
DEMetro_Z_vs_SMC 0.5 8.456 3.84e-06 2.441
DEMetro_Z_vs_SMC 0.9 13.099 4.7e-08 3.781
DEMetro_Z_vs_SMC 0.99 90.892 3.57e-17 26.238
HMC_vs_Metro 0.0 -0.438 0.67 -0.126
HMC_vs_Metro 0.3 -0.191 0.852 -0.055
HMC_vs_Metro 0.5 -0.301 0.769 -0.087
HMC_vs_Metro 0.9 -0.287 0.779 -0.083
HMC_vs_Metro 0.99 -2.824 0.0165 -0.815
Metro_vs_DEMetro_Z 0.0 1.320 0.214 0.381
Metro_vs_DEMetro_Z 0.3 2.364 0.0375 0.683
Metro_vs_DEMetro_Z 0.5 1.379 0.195 0.398
Metro_vs_DEMetro_Z 0.9 1.072 0.307 0.309
Metro_vs_DEMetro_Z 0.99 1.860 0.0898 0.537
HMC_vs_SMC 0.0 103.040 8.99e-18 29.745
HMC_vs_SMC 0.3 102.233 9.8e-18 29.512
HMC_vs_SMC 0.5 142.496 2.55e-19 41.135
HMC_vs_SMC 0.9 102.398 9.63e-18 29.560
HMC_vs_SMC 0.99 98.779 1.43e-17 28.515
Metro_vs_SMC 0.0 98.677 1.45e-17 28.486
Metro_vs_SMC 0.3 84.387 8.07e-17 24.360
Metro_vs_SMC 0.5 81.188 1.23e-16 23.437
Metro_vs_SMC 0.9 92.252 3.03e-17 26.631
Metro_vs_SMC 0.99 69.074 7.27e-16 19.940
HMC_vs_DEMetro_Z 0.0 1.283 0.226 0.370
HMC_vs_DEMetro_Z 0.3 2.496 0.0297 0.720
HMC_vs_DEMetro_Z 0.5 1.298 0.221 0.375
HMC_vs_DEMetro_Z 0.9 1.121 0.286 0.324
HMC_vs_DEMetro_Z 0.99 -0.828 0.425 -0.239
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.614 0.013 0.007 82.057
HMC 0.3 0.623 0.014 0.007 84.366
HMC 0.5 0.606 0.007 0.004 139.327
HMC 0.9 0.623 0.010 0.008 72.216
HMC 0.99 0.624 0.011 0.004 141.698
SMC 0.0 0.014 0.013 0.007 0.096
SMC 0.3 0.015 0.014 0.007 0.198
SMC 0.5 0.012 0.007 0.004 1.059
SMC 0.9 0.014 0.010 0.008 0.371
SMC 0.99 0.011 0.011 0.004 0.214
Metro 0.0 0.616 0.013 0.007 82.409
Metro 0.3 0.624 0.014 0.007 84.597
Metro 0.5 0.609 0.007 0.004 139.932
Metro 0.9 0.625 0.010 0.008 72.508
Metro 0.99 0.658 0.011 0.004 149.623
DEMetro_Z 0.0 0.533 0.013 0.007 70.982
DEMetro_Z 0.3 0.437 0.014 0.007 58.667
DEMetro_Z 0.5 0.529 0.007 0.004 121.358
DEMetro_Z 0.9 0.576 0.010 0.008 66.776
DEMetro_Z 0.99 0.633 0.011 0.004 143.740
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
0.0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.9 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.99 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0.0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.9 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.99 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.99
Chain
0.0
0.3
0.5
0.9
0.99

two_attr_dim

▼

Vary_Dimension_with_high_correlation (MvNormal, dimension, 12 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.063 0.95 0.028
HMC 5 3.864 0.00172 3.196
HMC 10 3.629 0.0019 2.013
HMC 15 2.861 0.0114 1.891
HMC 30 3.407 0.00519 4.652
SMC 2 -3.579 0.00238 -1.167
SMC 5 0.820 0.421 0.343
SMC 10 -0.007 0.994 -0.003
SMC 15 -0.704 0.489 -0.299
SMC 30 0.744 0.465 0.303
Metro 2 3.779 0.00274 6.182
Metro 5 6.493 4.17e-05 21.766
Metro 10 4.909 0.000444 15.768
Metro 15 4.845 0.000496 17.129
Metro 30 4.375 0.00109 22.776
DEMetro_Z 2 2.245 0.0396 1.520
DEMetro_Z 5 6.003 8.89e-05 788.290
DEMetro_Z 10 13.121 4.62e-08 499.307
DEMetro_Z 15 13.418 3.66e-08 486.752
DEMetro_Z 30 25.371 4.09e-11 594.295
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -2.698 0.0207 -0.779
HMC_vs_DEMetro_Z 1 -5.989 9.07e-05 -1.729
HMC_vs_DEMetro_Z 2 -13.045 4.91e-08 -3.766
HMC_vs_DEMetro_Z 3 -13.367 3.81e-08 -3.859
HMC_vs_DEMetro_Z 4 -25.249 4.33e-11 -7.289
Metro_vs_SMC 0 4.639 0.000718 1.339
Metro_vs_SMC 1 6.293 5.9e-05 1.817
Metro_vs_SMC 2 4.964 0.000426 1.433
Metro_vs_SMC 3 4.998 0.000403 1.443
Metro_vs_SMC 4 4.350 0.00115 1.256
Metro_vs_DEMetro_Z 0 3.604 0.00414 1.040
Metro_vs_DEMetro_Z 1 -5.752 0.000128 -1.660
Metro_vs_DEMetro_Z 2 -12.605 7.01e-08 -3.639
Metro_vs_DEMetro_Z 3 -12.828 5.84e-08 -3.703
Metro_vs_DEMetro_Z 4 -25.850 3.36e-11 -7.462
HMC_vs_Metro 0 -3.993 0.00211 -1.153
HMC_vs_Metro 1 -4.983 0.000413 -1.439
HMC_vs_Metro 2 -4.265 0.00133 -1.231
HMC_vs_Metro 3 -4.494 0.00091 -1.297
HMC_vs_Metro 4 -3.520 0.0048 -1.016
HMC_vs_SMC 0 2.979 0.0125 0.860
HMC_vs_SMC 1 3.730 0.00332 1.077
HMC_vs_SMC 2 3.139 0.00942 0.906
HMC_vs_SMC 3 3.619 0.00403 1.045
HMC_vs_SMC 4 3.001 0.0121 0.866
DEMetro_Z_vs_SMC 0 3.957 0.00225 1.142
DEMetro_Z_vs_SMC 1 5.998 8.95e-05 1.731
DEMetro_Z_vs_SMC 2 13.132 4.58e-08 3.791
DEMetro_Z_vs_SMC 3 13.434 3.62e-08 3.878
DEMetro_Z_vs_SMC 4 25.488 3.91e-11 7.358
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.028 0.028 0.014 0.028
HMC 5 0.039 0.015 0.007 3.196
HMC 10 0.038 0.015 0.012 2.013
HMC 15 0.046 0.024 0.012 1.891
HMC 30 0.071 0.018 0.011 4.652
SMC 2 0.012 0.028 0.014 -1.167
SMC 5 0.018 0.015 0.007 0.343
SMC 10 0.015 0.015 0.012 -0.003
SMC 15 0.020 0.024 0.012 -0.299
SMC 30 0.022 0.018 0.011 0.303
Metro 2 0.111 0.028 0.014 6.182
Metro 5 0.178 0.015 0.007 21.766
Metro 10 0.196 0.015 0.012 15.768
Metro 15 0.224 0.024 0.012 17.129
Metro 30 0.278 0.018 0.011 22.776
DEMetro_Z 2 0.048 0.028 0.014 1.520
DEMetro_Z 5 5.909 0.015 0.007 788.290
DEMetro_Z 10 5.759 0.015 0.012 499.307
DEMetro_Z 15 5.733 0.024 0.012 486.752
DEMetro_Z 30 6.803 0.018 0.011 594.295
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.080 0.00658 1.781
HMC 5 2.283 0.0413 3.032
HMC 10 1.449 0.164 0.798
HMC 15 2.337 0.0374 3.056
HMC 30 3.589 0.00346 3.969
SMC 2 1.421 0.17 0.660
SMC 5 1.347 0.195 0.747
SMC 10 -0.217 0.83 -0.089
SMC 15 0.189 0.852 0.079
SMC 30 -0.553 0.587 -0.185
Metro 2 5.150 0.00027 9.292
Metro 5 4.589 0.000759 18.741
Metro 10 3.457 0.00519 9.335
Metro 15 5.496 0.000174 15.615
Metro 30 5.886 9.05e-05 12.411
DEMetro_Z 2 3.592 0.0033 3.617
DEMetro_Z 5 6.652 3.6e-05 11814.735
DEMetro_Z 10 15.026 1.12e-08 6977.533
DEMetro_Z 15 36.536 7.78e-13 11280.894
DEMetro_Z 30 32.984 2.37e-12 9140.934
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 1.771 0.104 0.511
HMC_vs_SMC 1 1.675 0.122 0.484
HMC_vs_SMC 2 1.502 0.161 0.434
HMC_vs_SMC 3 2.693 0.0209 0.777
HMC_vs_SMC 4 4.033 0.00197 1.164
Metro_vs_DEMetro_Z 0 2.639 0.023 0.762
Metro_vs_DEMetro_Z 1 -6.643 3.65e-05 -1.918
Metro_vs_DEMetro_Z 2 -15.013 1.13e-08 -4.334
Metro_vs_DEMetro_Z 3 -36.756 7.29e-13 -10.611
Metro_vs_DEMetro_Z 4 -32.988 2.37e-12 -9.523
HMC_vs_Metro 0 -4.264 0.00133 -1.231
HMC_vs_Metro 1 -3.918 0.0024 -1.131
HMC_vs_Metro 2 -3.125 0.00967 -0.902
HMC_vs_Metro 3 -4.280 0.0013 -1.236
HMC_vs_Metro 4 -3.613 0.00408 -1.043
HMC_vs_DEMetro_Z 0 -1.477 0.168 -0.426
HMC_vs_DEMetro_Z 1 -6.651 3.61e-05 -1.920
HMC_vs_DEMetro_Z 2 -15.026 1.12e-08 -4.338
HMC_vs_DEMetro_Z 3 -36.581 7.68e-13 -10.560
HMC_vs_DEMetro_Z 4 -32.957 2.4e-12 -9.514
Metro_vs_SMC 0 4.997 0.000404 1.443
Metro_vs_SMC 1 4.274 0.00131 1.234
Metro_vs_SMC 2 3.413 0.0058 0.985
Metro_vs_SMC 3 5.502 0.000186 1.588
Metro_vs_SMC 4 6.104 7.69e-05 1.762
DEMetro_Z_vs_SMC 0 3.434 0.00558 0.991
DEMetro_Z_vs_SMC 1 6.651 3.6e-05 1.920
DEMetro_Z_vs_SMC 2 15.027 1.12e-08 4.338
DEMetro_Z_vs_SMC 3 36.547 7.76e-13 10.550
DEMetro_Z_vs_SMC 4 32.971 2.38e-12 9.518
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.034 0.017 0.009 1.781
HMC 5 0.059 0.025 0.011 3.032
HMC 10 0.047 0.032 0.019 0.798
HMC 15 0.059 0.024 0.011 3.056
HMC 30 0.108 0.032 0.019 3.969
SMC 2 0.024 0.017 0.009 0.660
SMC 5 0.034 0.025 0.011 0.747
SMC 10 0.030 0.032 0.019 -0.089
SMC 15 0.025 0.024 0.011 0.079
SMC 30 0.029 0.032 0.019 -0.185
Metro 2 0.106 0.017 0.009 9.292
Metro 5 0.236 0.025 0.011 18.741
Metro 10 0.206 0.032 0.019 9.335
Metro 15 0.202 0.024 0.011 15.615
Metro 30 0.268 0.032 0.019 12.411
DEMetro_Z 2 0.052 0.017 0.009 3.617
DEMetro_Z 5 132.997 0.025 0.011 11814.735
DEMetro_Z 10 130.624 0.032 0.019 6977.533
DEMetro_Z 15 128.779 0.024 0.011 11280.894
DEMetro_Z 30 173.820 0.032 0.019 9140.934
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.579 0.569 0.265
HMC 5 5.441 9.98e-05 4.922
HMC 10 4.844 0.000102 2.431
HMC 15 3.951 0.00148 3.356
HMC 30 4.362 0.00103 8.955
SMC 2 -3.411 0.00309 -1.152
SMC 5 1.300 0.207 0.573
SMC 10 0.271 0.789 0.110
SMC 15 0.234 0.817 0.102
SMC 30 1.647 0.114 0.640
Metro 2 4.682 0.000602 9.628
Metro 5 8.316 4.1e-06 28.169
Metro 10 5.227 0.000275 23.088
Metro 15 6.589 3.76e-05 28.134
Metro 30 5.459 0.000196 39.285
DEMetro_Z 2 2.909 0.0111 2.227
DEMetro_Z 5 14.712 1.4e-08 1748.594
DEMetro_Z 10 26.026 3.12e-11 1344.941
DEMetro_Z 15 36.101 8.85e-13 1363.419
DEMetro_Z 30 49.751 2.65e-14 1812.153
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 4.098 0.00177 1.183
Metro_vs_DEMetro_Z 1 -14.348 1.82e-08 -4.142
Metro_vs_DEMetro_Z 2 -25.610 3.71e-11 -7.393
Metro_vs_DEMetro_Z 3 -34.707 1.36e-12 -10.019
Metro_vs_DEMetro_Z 4 -51.334 1.89e-14 -14.819
DEMetro_Z_vs_SMC 0 5.247 0.000274 1.515
DEMetro_Z_vs_SMC 1 14.697 1.41e-08 4.243
DEMetro_Z_vs_SMC 2 26.085 3.04e-11 7.530
DEMetro_Z_vs_SMC 3 36.122 8.81e-13 10.428
DEMetro_Z_vs_SMC 4 49.866 2.59e-14 14.395
HMC_vs_DEMetro_Z 0 -2.489 0.0301 -0.719
HMC_vs_DEMetro_Z 1 -14.708 1.4e-08 -4.246
HMC_vs_DEMetro_Z 2 -25.928 3.25e-11 -7.485
HMC_vs_DEMetro_Z 3 -35.893 9.44e-13 -10.361
HMC_vs_DEMetro_Z 4 -49.152 3.03e-14 -14.189
HMC_vs_Metro 0 -4.688 0.000663 -1.353
HMC_vs_Metro 1 -6.483 4.53e-05 -1.871
HMC_vs_Metro 2 -4.586 0.000782 -1.324
HMC_vs_Metro 3 -6.001 8.91e-05 -1.732
HMC_vs_Metro 4 -4.069 0.00185 -1.175
HMC_vs_SMC 0 4.071 0.00185 1.175
HMC_vs_SMC 1 4.665 0.000688 1.347
HMC_vs_SMC 2 4.740 0.000609 1.368
HMC_vs_SMC 3 4.130 0.00167 1.192
HMC_vs_SMC 4 3.901 0.00247 1.126
Metro_vs_SMC 0 5.524 0.00018 1.595
Metro_vs_SMC 1 8.198 5.17e-06 2.367
Metro_vs_SMC 2 5.163 0.000312 1.490
Metro_vs_SMC 3 6.574 4e-05 1.898
Metro_vs_SMC 4 5.374 0.000225 1.551
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.036 0.033 0.009 0.265
HMC 5 0.047 0.022 0.005 4.922
HMC 10 0.040 0.023 0.007 2.431
HMC 15 0.047 0.025 0.007 3.356
HMC 30 0.076 0.024 0.006 8.955
SMC 2 0.023 0.033 0.009 -1.152
SMC 5 0.025 0.022 0.005 0.573
SMC 10 0.024 0.023 0.007 0.110
SMC 15 0.026 0.025 0.007 0.102
SMC 30 0.027 0.024 0.006 0.640
Metro 2 0.118 0.033 0.009 9.628
Metro 5 0.162 0.022 0.005 28.169
Metro 10 0.179 0.023 0.007 23.088
Metro 15 0.210 0.025 0.007 28.134
Metro 30 0.251 0.024 0.006 39.285
DEMetro_Z 2 0.053 0.033 0.009 2.227
DEMetro_Z 5 8.707 0.022 0.005 1748.594
DEMetro_Z 10 9.095 0.023 0.007 1344.941
DEMetro_Z 15 8.973 0.025 0.007 1363.419
DEMetro_Z 30 10.516 0.024 0.006 1812.153
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.972 0.345 0.586
HMC 5 4.856 0.000291 4.487
HMC 10 3.789 0.0011 1.794
HMC 15 3.969 0.00129 3.002
HMC 30 4.254 0.00118 7.022
SMC 2 -3.023 0.00647 -1.120
SMC 5 1.876 0.0745 0.851
SMC 10 -0.269 0.79 -0.099
SMC 15 0.431 0.671 0.159
SMC 30 1.721 0.0997 0.652
Metro 2 5.141 0.00028 9.983
Metro 5 7.500 1.06e-05 20.948
Metro 10 4.884 0.00047 19.642
Metro 15 8.381 3.48e-06 20.680
Metro 30 5.879 0.000103 28.023
DEMetro_Z 2 2.983 0.0105 2.895
DEMetro_Z 5 42.389 1.23e-13 176.970
DEMetro_Z 10 29.628 6.17e-12 114.880
DEMetro_Z 15 30.613 4.14e-12 109.167
DEMetro_Z 30 50.547 1.06e-14 120.362
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 5.316 0.000246 1.535
DEMetro_Z_vs_SMC 1 43.310 1.21e-13 12.502
DEMetro_Z_vs_SMC 2 30.111 6.4e-12 8.692
DEMetro_Z_vs_SMC 3 30.154 6.31e-12 8.705
DEMetro_Z_vs_SMC 4 51.780 1.71e-14 14.948
HMC_vs_Metro 0 -4.830 0.000528 -1.394
HMC_vs_Metro 1 -5.710 0.000136 -1.648
HMC_vs_Metro 2 -4.274 0.00131 -1.234
HMC_vs_Metro 3 -7.271 1.6e-05 -2.099
HMC_vs_Metro 4 -4.152 0.00161 -1.199
Metro_vs_DEMetro_Z 0 3.877 0.00257 1.119
Metro_vs_DEMetro_Z 1 -30.748 5.1e-12 -8.876
Metro_vs_DEMetro_Z 2 -14.392 1.76e-08 -4.155
Metro_vs_DEMetro_Z 3 -18.986 9.33e-10 -5.481
Metro_vs_DEMetro_Z 4 -21.009 3.15e-10 -6.065
HMC_vs_SMC 0 3.117 0.0098 0.900
HMC_vs_SMC 1 4.487 0.000921 1.295
HMC_vs_SMC 2 6.133 7.38e-05 1.770
HMC_vs_SMC 3 4.131 0.00167 1.193
HMC_vs_SMC 4 3.816 0.00286 1.101
Metro_vs_SMC 0 5.993 9.01e-05 1.730
Metro_vs_SMC 1 7.352 1.44e-05 2.122
Metro_vs_SMC 2 4.824 0.000532 1.393
Metro_vs_SMC 3 8.490 3.7e-06 2.451
Metro_vs_SMC 4 5.700 0.000138 1.645
HMC_vs_DEMetro_Z 0 -2.149 0.0547 -0.620
HMC_vs_DEMetro_Z 1 -45.183 7.63e-14 -13.043
HMC_vs_DEMetro_Z 2 -28.728 1.07e-11 -8.293
HMC_vs_DEMetro_Z 3 -29.096 9.3e-12 -8.399
HMC_vs_DEMetro_Z 4 -35.351 1.12e-12 -10.205
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.020 0.017 0.005 0.586
HMC 5 0.029 0.012 0.004 4.487
HMC 10 0.023 0.014 0.005 1.794
HMC 15 0.030 0.014 0.005 3.002
HMC 30 0.047 0.014 0.005 7.022
SMC 2 0.012 0.017 0.005 -1.120
SMC 5 0.015 0.012 0.004 0.851
SMC 10 0.013 0.014 0.005 -0.099
SMC 15 0.015 0.014 0.005 0.159
SMC 30 0.017 0.014 0.005 0.652
Metro 2 0.065 0.017 0.005 9.983
Metro 5 0.093 0.012 0.004 20.948
Metro 10 0.117 0.014 0.005 19.642
Metro 15 0.125 0.014 0.005 20.680
Metro 30 0.145 0.014 0.005 28.023
DEMetro_Z 2 0.031 0.017 0.005 2.895
DEMetro_Z 5 0.699 0.012 0.004 176.970
DEMetro_Z 10 0.619 0.014 0.005 114.880
DEMetro_Z 15 0.597 0.014 0.005 109.167
DEMetro_Z 30 0.577 0.014 0.005 120.362
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -0.747 0.464 -0.356
HMC 5 2.880 0.0132 3.177
HMC 10 3.319 0.00478 2.489
HMC 15 3.532 0.00384 3.891
HMC 30 2.893 0.0143 8.044
SMC 2 -0.601 0.554 -0.265
SMC 5 0.636 0.532 0.305
SMC 10 0.335 0.74 0.147
SMC 15 0.250 0.805 0.135
SMC 30 0.484 0.633 0.194
Metro 2 3.644 0.0033 4.715
Metro 5 4.477 0.00091 17.139
Metro 10 4.355 0.00113 24.063
Metro 15 3.710 0.0034 16.555
Metro 30 4.132 0.00165 25.481
DEMetro_Z 2 1.491 0.154 0.905
DEMetro_Z 5 5.557 0.000171 770.265
DEMetro_Z 10 14.147 2.11e-08 811.952
DEMetro_Z 15 14.128 2.14e-08 880.405
DEMetro_Z 30 31.292 4.2e-12 1077.892
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -2.067 0.0631 -0.597
HMC_vs_DEMetro_Z 1 -5.517 0.000181 -1.593
HMC_vs_DEMetro_Z 2 -14.175 2.06e-08 -4.092
HMC_vs_DEMetro_Z 3 -14.145 2.11e-08 -4.083
HMC_vs_DEMetro_Z 4 -30.472 5.63e-12 -8.796
Metro_vs_SMC 0 4.377 0.0011 1.264
Metro_vs_SMC 1 4.334 0.00119 1.251
Metro_vs_SMC 2 4.517 0.000877 1.304
Metro_vs_SMC 3 3.702 0.00349 1.069
Metro_vs_SMC 4 4.025 0.002 1.162
Metro_vs_DEMetro_Z 0 3.330 0.00671 0.961
Metro_vs_DEMetro_Z 1 -5.478 0.000193 -1.581
Metro_vs_DEMetro_Z 2 -13.677 3e-08 -3.948
Metro_vs_DEMetro_Z 3 -14.075 2.22e-08 -4.063
Metro_vs_DEMetro_Z 4 -32.286 3e-12 -9.320
HMC_vs_Metro 0 -3.816 0.00286 -1.102
HMC_vs_Metro 1 -3.525 0.00476 -1.018
HMC_vs_Metro 2 -3.922 0.00238 -1.132
HMC_vs_Metro 3 -2.806 0.0171 -0.810
HMC_vs_Metro 4 -3.361 0.00635 -0.970
HMC_vs_SMC 0 -0.170 0.868 -0.049
HMC_vs_SMC 1 2.564 0.0263 0.740
HMC_vs_SMC 2 3.201 0.00844 0.924
HMC_vs_SMC 3 3.201 0.00845 0.924
HMC_vs_SMC 4 2.748 0.019 0.793
DEMetro_Z_vs_SMC 0 2.003 0.0704 0.578
DEMetro_Z_vs_SMC 1 5.558 0.000171 1.604
DEMetro_Z_vs_SMC 2 14.129 2.14e-08 4.079
DEMetro_Z_vs_SMC 3 14.182 2.05e-08 4.094
DEMetro_Z_vs_SMC 4 31.270 4.25e-12 9.027
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.023 0.028 0.014 -0.356
HMC 5 0.039 0.015 0.007 3.177
HMC 10 0.044 0.015 0.012 2.489
HMC 15 0.069 0.024 0.012 3.891
HMC 30 0.110 0.018 0.011 8.044
SMC 2 0.024 0.028 0.014 -0.265
SMC 5 0.017 0.015 0.007 0.305
SMC 10 0.017 0.015 0.012 0.147
SMC 15 0.025 0.024 0.012 0.135
SMC 30 0.020 0.018 0.011 0.194
Metro 2 0.092 0.028 0.014 4.715
Metro 5 0.143 0.015 0.007 17.139
Metro 10 0.292 0.015 0.012 24.063
Metro 15 0.218 0.024 0.012 16.555
Metro 30 0.309 0.018 0.011 25.481
DEMetro_Z 2 0.040 0.028 0.014 0.905
DEMetro_Z 5 5.774 0.015 0.007 770.265
DEMetro_Z 10 9.356 0.015 0.012 811.952
DEMetro_Z 15 10.350 0.024 0.012 880.405
DEMetro_Z 30 12.323 0.018 0.011 1077.892
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.107 0.00865 3.478
HMC 5 2.209 0.0452 2.032
HMC 10 1.626 0.126 1.296
HMC 15 3.496 0.00423 4.158
HMC 30 3.463 0.00413 3.321
SMC 2 1.382 0.184 0.803
SMC 5 0.085 0.933 0.044
SMC 10 -1.064 0.303 -0.339
SMC 15 0.533 0.6 0.255
SMC 30 -1.360 0.191 -0.453
Metro 2 2.826 0.0162 7.891
Metro 5 4.326 0.00106 7.535
Metro 10 2.905 0.0139 6.960
Metro 15 3.390 0.00596 14.888
Metro 30 6.134 6.68e-05 16.526
DEMetro_Z 2 3.447 0.00405 2.997
DEMetro_Z 5 3.661 0.00375 3797.819
DEMetro_Z 10 6.896 2.6e-05 1131.907
DEMetro_Z 15 7.473 1.24e-05 1656.744
DEMetro_Z 30 9.182 1.72e-06 1001.186
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 3.010 0.0119 0.869
HMC_vs_SMC 1 1.887 0.0858 0.545
HMC_vs_SMC 2 1.973 0.0741 0.570
HMC_vs_SMC 3 3.307 0.00699 0.955
HMC_vs_SMC 4 3.923 0.00238 1.132
Metro_vs_DEMetro_Z 0 1.843 0.0924 0.532
Metro_vs_DEMetro_Z 1 -3.650 0.00382 -1.054
Metro_vs_DEMetro_Z 2 -6.829 2.84e-05 -1.971
Metro_vs_DEMetro_Z 3 -7.369 1.41e-05 -2.127
Metro_vs_DEMetro_Z 4 -9.085 1.91e-06 -2.623
HMC_vs_Metro 0 -1.368 0.198 -0.395
HMC_vs_Metro 1 -3.475 0.00519 -1.003
HMC_vs_Metro 2 -2.224 0.048 -0.642
HMC_vs_Metro 3 -2.418 0.0341 -0.698
HMC_vs_Metro 4 -4.700 0.000651 -1.357
HMC_vs_DEMetro_Z 0 0.386 0.707 0.111
HMC_vs_DEMetro_Z 1 -3.657 0.00377 -1.056
HMC_vs_DEMetro_Z 2 -6.869 2.7e-05 -1.983
HMC_vs_DEMetro_Z 3 -7.457 1.27e-05 -2.153
HMC_vs_DEMetro_Z 4 -9.168 1.75e-06 -2.646
Metro_vs_SMC 0 2.506 0.0292 0.723
Metro_vs_SMC 1 3.814 0.00288 1.101
Metro_vs_SMC 2 3.108 0.00996 0.897
Metro_vs_SMC 3 3.205 0.00838 0.925
Metro_vs_SMC 4 6.430 4.87e-05 1.856
DEMetro_Z_vs_SMC 0 2.383 0.0363 0.688
DEMetro_Z_vs_SMC 1 3.661 0.00375 1.057
DEMetro_Z_vs_SMC 2 6.899 2.59e-05 1.992
DEMetro_Z_vs_SMC 3 7.482 1.23e-05 2.160
DEMetro_Z_vs_SMC 4 9.182 1.72e-06 2.651
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.050 0.017 0.009 3.478
HMC 5 0.048 0.025 0.011 2.032
HMC 10 0.056 0.032 0.019 1.296
HMC 15 0.071 0.024 0.011 4.158
HMC 30 0.096 0.032 0.019 3.321
SMC 2 0.025 0.017 0.009 0.803
SMC 5 0.026 0.025 0.011 0.044
SMC 10 0.025 0.032 0.019 -0.339
SMC 15 0.027 0.024 0.011 0.255
SMC 30 0.024 0.032 0.019 -0.453
Metro 2 0.092 0.017 0.009 7.891
Metro 5 0.110 0.025 0.011 7.535
Metro 10 0.162 0.032 0.019 6.960
Metro 15 0.194 0.024 0.011 14.888
Metro 30 0.347 0.032 0.019 16.526
DEMetro_Z 2 0.046 0.017 0.009 2.997
DEMetro_Z 5 42.769 0.025 0.011 3797.819
DEMetro_Z 10 21.217 0.032 0.019 1131.907
DEMetro_Z 15 18.933 0.024 0.011 1656.744
DEMetro_Z 30 19.067 0.032 0.019 1001.186
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.334 0.742 0.179
HMC 5 3.670 0.00292 3.930
HMC 10 4.969 0.000191 3.891
HMC 15 4.864 0.000369 6.103
HMC 30 3.050 0.0109 12.884
SMC 2 -0.552 0.587 -0.259
SMC 5 0.636 0.533 0.357
SMC 10 -0.215 0.832 -0.097
SMC 15 0.877 0.393 0.536
SMC 30 1.028 0.315 0.454
Metro 2 4.643 0.000607 7.675
Metro 5 5.040 0.000369 22.687
Metro 10 4.742 0.000603 35.314
Metro 15 5.203 0.000288 29.016
Metro 30 5.704 0.000136 47.958
DEMetro_Z 2 2.090 0.054 1.496
DEMetro_Z 5 5.376 0.000225 1044.981
DEMetro_Z 10 13.246 4.19e-08 1223.253
DEMetro_Z 15 15.029 1.12e-08 1353.310
DEMetro_Z 30 25.785 3.45e-11 1760.089
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 4.289 0.00128 1.238
Metro_vs_DEMetro_Z 1 -5.299 0.000253 -1.530
Metro_vs_DEMetro_Z 2 -12.843 5.77e-08 -3.707
Metro_vs_DEMetro_Z 3 -14.934 1.19e-08 -4.311
Metro_vs_DEMetro_Z 4 -26.054 3.08e-11 -7.521
DEMetro_Z_vs_SMC 0 2.913 0.0141 0.841
DEMetro_Z_vs_SMC 1 5.376 0.000225 1.552
DEMetro_Z_vs_SMC 2 13.231 4.24e-08 3.819
DEMetro_Z_vs_SMC 3 15.072 1.08e-08 4.351
DEMetro_Z_vs_SMC 4 25.760 3.49e-11 7.436
HMC_vs_DEMetro_Z 0 -2.059 0.064 -0.594
HMC_vs_DEMetro_Z 1 -5.342 0.000237 -1.542
HMC_vs_DEMetro_Z 2 -13.211 4.31e-08 -3.814
HMC_vs_DEMetro_Z 3 -15.017 1.13e-08 -4.335
HMC_vs_DEMetro_Z 4 -25.469 3.94e-11 -7.352
HMC_vs_Metro 0 -4.939 0.000443 -1.426
HMC_vs_Metro 1 -3.934 0.00234 -1.136
HMC_vs_Metro 2 -4.164 0.00158 -1.202
HMC_vs_Metro 3 -3.839 0.00275 -1.108
HMC_vs_Metro 4 -4.695 0.000655 -1.355
HMC_vs_SMC 0 1.172 0.266 0.338
HMC_vs_SMC 1 3.304 0.00703 0.954
HMC_vs_SMC 2 5.146 0.00032 1.486
HMC_vs_SMC 3 3.893 0.00251 1.124
HMC_vs_SMC 4 2.876 0.0151 0.830
Metro_vs_SMC 0 5.423 0.000209 1.565
Metro_vs_SMC 1 4.752 0.000598 1.372
Metro_vs_SMC 2 4.908 0.000466 1.417
Metro_vs_SMC 3 5.135 0.000326 1.482
Metro_vs_SMC 4 5.614 0.000157 1.621
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.035 0.033 0.009 0.179
HMC 5 0.042 0.022 0.005 3.930
HMC 10 0.050 0.023 0.007 3.891
HMC 15 0.065 0.025 0.007 6.103
HMC 30 0.098 0.024 0.006 12.884
SMC 2 0.031 0.033 0.009 -0.259
SMC 5 0.024 0.022 0.005 0.357
SMC 10 0.023 0.023 0.007 -0.097
SMC 15 0.029 0.025 0.007 0.536
SMC 30 0.026 0.024 0.006 0.454
Metro 2 0.101 0.033 0.009 7.675
Metro 5 0.135 0.022 0.005 22.687
Metro 10 0.261 0.023 0.007 35.314
Metro 15 0.216 0.025 0.007 29.016
Metro 30 0.301 0.024 0.006 47.958
DEMetro_Z 2 0.046 0.033 0.009 1.496
DEMetro_Z 5 5.212 0.022 0.005 1044.981
DEMetro_Z 10 8.274 0.023 0.007 1223.253
DEMetro_Z 15 8.907 0.025 0.007 1353.310
DEMetro_Z 30 10.215 0.024 0.006 1760.089
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.312 0.759 0.218
HMC 5 3.704 0.00261 3.595
HMC 10 4.594 0.000312 3.083
HMC 15 5.355 0.000102 4.426
HMC 30 2.819 0.0164 8.435
SMC 2 -0.418 0.68 -0.172
SMC 5 0.562 0.58 0.271
SMC 10 -1.210 0.239 -0.467
SMC 15 0.536 0.598 0.284
SMC 30 0.792 0.437 0.345
Metro 2 5.841 8.29e-05 8.613
Metro 5 5.550 0.000162 16.719
Metro 10 5.560 0.000166 28.051
Metro 15 6.024 8.3e-05 25.286
Metro 30 7.076 2e-05 40.571
DEMetro_Z 2 1.615 0.127 1.129
DEMetro_Z 5 11.435 1.89e-07 150.159
DEMetro_Z 10 35.098 1.04e-12 173.085
DEMetro_Z 15 56.083 4.43e-15 169.724
DEMetro_Z 30 43.859 8.81e-14 203.778
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 2.503 0.0293 0.723
DEMetro_Z_vs_SMC 1 11.302 2.15e-07 3.262
DEMetro_Z_vs_SMC 2 35.004 1.24e-12 10.105
DEMetro_Z_vs_SMC 3 56.154 7.05e-15 16.210
DEMetro_Z_vs_SMC 4 45.179 7.64e-14 13.042
HMC_vs_Metro 0 -6.099 7.74e-05 -1.761
HMC_vs_Metro 1 -3.964 0.00222 -1.144
HMC_vs_Metro 2 -4.816 0.000539 -1.390
HMC_vs_Metro 3 -4.693 0.000658 -1.355
HMC_vs_Metro 4 -6.364 5.34e-05 -1.837
Metro_vs_DEMetro_Z 0 6.747 3.17e-05 1.948
Metro_vs_DEMetro_Z 1 -11.172 2.42e-07 -3.225
Metro_vs_DEMetro_Z 2 -18.585 1.17e-09 -5.365
Metro_vs_DEMetro_Z 3 -29.836 7.08e-12 -8.613
Metro_vs_DEMetro_Z 4 -18.991 9.31e-10 -5.482
HMC_vs_SMC 0 0.820 0.43 0.237
HMC_vs_SMC 1 4.039 0.00195 1.166
HMC_vs_SMC 2 5.809 0.000118 1.677
HMC_vs_SMC 3 4.362 0.00113 1.259
HMC_vs_SMC 4 2.650 0.0226 0.765
Metro_vs_SMC 0 6.698 3.38e-05 1.934
Metro_vs_SMC 1 5.090 0.00035 1.469
Metro_vs_SMC 2 5.794 0.00012 1.673
Metro_vs_SMC 3 5.976 9.24e-05 1.725
Metro_vs_SMC 4 6.976 2.34e-05 2.014
HMC_vs_DEMetro_Z 0 -1.471 0.169 -0.425
HMC_vs_DEMetro_Z 1 -11.154 2.46e-07 -3.220
HMC_vs_DEMetro_Z 2 -33.810 1.81e-12 -9.760
HMC_vs_DEMetro_Z 3 -50.272 2.37e-14 -14.512
HMC_vs_DEMetro_Z 4 -29.980 6.71e-12 -8.655
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.018 0.017 0.005 0.218
HMC 5 0.026 0.012 0.004 3.595
HMC 10 0.030 0.014 0.005 3.083
HMC 15 0.038 0.014 0.005 4.426
HMC 30 0.053 0.014 0.005 8.435
SMC 2 0.017 0.017 0.005 -0.172
SMC 5 0.013 0.012 0.004 0.271
SMC 10 0.011 0.014 0.005 -0.467
SMC 15 0.016 0.014 0.005 0.284
SMC 30 0.016 0.014 0.005 0.345
Metro 2 0.059 0.017 0.005 8.613
Metro 5 0.077 0.012 0.004 16.719
Metro 10 0.162 0.014 0.005 28.051
Metro 15 0.149 0.014 0.005 25.286
Metro 30 0.204 0.014 0.005 40.571
DEMetro_Z 2 0.023 0.017 0.005 1.129
DEMetro_Z 5 0.595 0.012 0.004 150.159
DEMetro_Z 10 0.925 0.014 0.005 173.085
DEMetro_Z 15 0.921 0.014 0.005 169.724
DEMetro_Z 30 0.967 0.014 0.005 203.778
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
2 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
30 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
30 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2
5
10
15
30
Chain
2
5
10
15
30

Vary_Dimension_with_heavy_Tails (MvStudentT, dimension, 12 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -1.109 0.28 -0.409
HMC 5 1.132 0.277 0.961
HMC 10 1.520 0.156 3.018
HMC 15 0.379 0.709 0.209
HMC 30 1.118 0.287 33.826
SMC 2 -0.602 0.555 -0.196
SMC 5 4.519 0.000687 5.952
SMC 10 6.429 3.96e-05 12.364
SMC 15 9.854 1.27e-08 5.627
SMC 30 15.641 1.07e-09 16.561
Metro 2 0.661 0.516 0.282
Metro 5 4.958 0.000104 2.809
Metro 10 4.151 0.00133 5.565
Metro 15 2.852 0.0112 1.757
Metro 30 3.777 0.00302 17.125
DEMetro_Z 2 1.784 0.0883 0.751
DEMetro_Z 5 5.149 0.000319 141.883
DEMetro_Z 10 5.190 0.000299 150.517
DEMetro_Z 15 8.244 4.8e-06 59.111
DEMetro_Z 30 11.501 1.8e-07 767.340
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -3.285 0.00727 -0.948
HMC_vs_DEMetro_Z 1 -5.094 0.000347 -1.470
HMC_vs_DEMetro_Z 2 -5.078 0.000356 -1.466
HMC_vs_DEMetro_Z 3 -8.195 5.19e-06 -2.366
HMC_vs_DEMetro_Z 4 -10.464 4.69e-07 -3.021
Metro_vs_SMC 0 1.739 0.11 0.502
Metro_vs_SMC 1 -2.372 0.0371 -0.685
Metro_vs_SMC 2 -2.577 0.0257 -0.744
Metro_vs_SMC 3 -5.668 0.000145 -1.636
Metro_vs_SMC 4 0.130 0.899 0.037
Metro_vs_DEMetro_Z 0 -1.066 0.309 -0.308
Metro_vs_DEMetro_Z 1 -5.001 0.000402 -1.444
Metro_vs_DEMetro_Z 2 -4.961 0.000428 -1.432
Metro_vs_DEMetro_Z 3 -8.115 5.7e-06 -2.343
Metro_vs_DEMetro_Z 4 -11.010 2.8e-07 -3.178
HMC_vs_Metro 0 -2.116 0.058 -0.611
HMC_vs_Metro 1 -2.020 0.0684 -0.583
HMC_vs_Metro 2 -1.825 0.0953 -0.527
HMC_vs_Metro 3 -2.213 0.0489 -0.639
HMC_vs_Metro 4 0.528 0.608 0.152
HMC_vs_SMC 0 -0.920 0.377 -0.266
HMC_vs_SMC 1 -3.077 0.0105 -0.888
HMC_vs_SMC 2 -3.577 0.00434 -1.033
HMC_vs_SMC 3 -8.477 3.75e-06 -2.447
HMC_vs_SMC 4 0.570 0.58 0.165
DEMetro_Z_vs_SMC 0 3.024 0.0116 0.873
DEMetro_Z_vs_SMC 1 4.913 0.000462 1.418
DEMetro_Z_vs_SMC 2 4.638 0.000719 1.339
DEMetro_Z_vs_SMC 3 7.287 1.57e-05 2.104
DEMetro_Z_vs_SMC 4 11.230 2.29e-07 3.242
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.056 0.072 0.040 -0.409
HMC 5 0.076 0.053 0.023 0.961
HMC 10 0.109 0.065 0.015 3.018
HMC 15 0.080 0.073 0.032 0.209
HMC 30 0.342 0.066 0.008 33.826
SMC 2 0.064 0.072 0.040 -0.196
SMC 5 0.191 0.053 0.023 5.952
SMC 10 0.247 0.065 0.015 12.364
SMC 15 0.252 0.073 0.032 5.627
SMC 30 0.201 0.066 0.008 16.561
Metro 2 0.083 0.072 0.040 0.282
Metro 5 0.118 0.053 0.023 2.809
Metro 10 0.147 0.065 0.015 5.565
Metro 15 0.129 0.073 0.032 1.757
Metro 30 0.206 0.066 0.008 17.125
DEMetro_Z 2 0.102 0.072 0.040 0.751
DEMetro_Z 5 3.329 0.053 0.023 141.883
DEMetro_Z 10 2.282 0.065 0.015 150.517
DEMetro_Z 15 1.957 0.073 0.032 59.111
DEMetro_Z 30 6.342 0.066 0.008 767.340
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -0.030 0.976 -0.012
HMC 5 -0.360 0.723 -0.138
HMC 10 1.626 0.132 4.841
HMC 15 -0.894 0.387 -0.273
HMC 30 1.075 0.305 9.498
SMC 2 -0.071 0.944 -0.027
SMC 5 3.343 0.00408 2.160
SMC 10 17.480 3.59e-11 13.379
SMC 15 5.240 0.000178 1.566
SMC 30 32.543 1.13e-14 26.465
Metro 2 -0.130 0.898 -0.049
Metro 5 -1.486 0.159 -0.460
Metro 10 2.062 0.0584 1.733
Metro 15 -1.257 0.233 -0.371
Metro 30 1.036 0.322 4.254
DEMetro_Z 2 0.035 0.973 0.014
DEMetro_Z 5 3.512 0.00487 141.501
DEMetro_Z 10 3.759 0.00316 60.947
DEMetro_Z 15 3.578 0.00305 2.993
DEMetro_Z 30 8.425 3.96e-06 151.735
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.514 0.618 0.148
HMC_vs_SMC 1 -3.434 0.00558 -0.991
HMC_vs_SMC 2 -2.415 0.0343 -0.697
HMC_vs_SMC 3 -15.661 7.23e-09 -4.521
HMC_vs_SMC 4 -1.924 0.0806 -0.555
Metro_vs_DEMetro_Z 0 -1.879 0.087 -0.542
Metro_vs_DEMetro_Z 1 -3.521 0.00479 -1.016
Metro_vs_DEMetro_Z 2 -3.627 0.00398 -1.047
Metro_vs_DEMetro_Z 3 -4.255 0.00135 -1.228
Metro_vs_DEMetro_Z 4 -7.502 1.2e-05 -2.166
HMC_vs_Metro 0 0.822 0.428 0.237
HMC_vs_Metro 1 1.180 0.263 0.341
HMC_vs_Metro 2 1.003 0.338 0.289
HMC_vs_Metro 3 1.014 0.333 0.293
HMC_vs_Metro 4 0.517 0.615 0.149
HMC_vs_DEMetro_Z 0 -0.487 0.636 -0.141
HMC_vs_DEMetro_Z 1 -3.523 0.00477 -1.017
HMC_vs_DEMetro_Z 2 -4.083 0.00181 -1.179
HMC_vs_DEMetro_Z 3 -4.393 0.00108 -1.268
HMC_vs_DEMetro_Z 4 -8.159 5.42e-06 -2.355
Metro_vs_SMC 0 -0.378 0.712 -0.109
Metro_vs_SMC 1 -4.847 0.000513 -1.399
Metro_vs_SMC 2 -11.526 1.76e-07 -3.327
Metro_vs_SMC 3 -17.453 2.29e-09 -5.038
Metro_vs_SMC 4 -5.169 0.000309 -1.492
DEMetro_Z_vs_SMC 0 0.599 0.562 0.173
DEMetro_Z_vs_SMC 1 3.460 0.00533 0.999
DEMetro_Z_vs_SMC 2 2.862 0.0155 0.826
DEMetro_Z_vs_SMC 3 1.823 0.0956 0.526
DEMetro_Z_vs_SMC 4 7.037 2.16e-05 2.031
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 8.602 8.779 15.112 -0.012
HMC 5 4.400 5.105 5.103 -0.138
HMC 10 19.832 3.930 3.285 4.841
HMC 15 9.277 17.964 31.848 -0.273
HMC 30 39.346 4.774 3.640 9.498
SMC 2 8.370 8.779 15.112 -0.027
SMC 5 16.128 5.105 5.103 2.160
SMC 10 47.875 3.930 3.285 13.379
SMC 15 67.838 17.964 31.848 1.566
SMC 30 101.103 4.774 3.640 26.465
Metro 2 8.038 8.779 15.112 -0.049
Metro 5 2.760 5.105 5.103 -0.460
Metro 10 9.620 3.930 3.285 1.733
Metro 15 6.141 17.964 31.848 -0.371
Metro 30 20.259 4.774 3.640 4.254
DEMetro_Z 2 8.987 8.779 15.112 0.014
DEMetro_Z 5 727.202 5.105 5.103 141.501
DEMetro_Z 10 204.123 3.930 3.285 60.947
DEMetro_Z 15 113.275 17.964 31.848 2.993
DEMetro_Z 30 557.075 4.774 3.640 151.735
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 1.815 0.0847 0.902
HMC 5 3.277 0.00681 5.310
HMC 10 3.058 0.0108 14.158
HMC 15 3.023 0.0105 3.882
HMC 30 1.566 0.146 73.364
SMC 2 0.780 0.444 0.328
SMC 5 10.543 4.24e-07 79.507
SMC 10 28.772 1.02e-11 291.834
SMC 15 41.413 1.32e-13 127.591
SMC 30 72.168 4.13e-16 546.646
Metro 2 3.066 0.00636 1.611
Metro 5 5.330 0.000142 5.485
Metro 10 4.306 0.00121 16.898
Metro 15 3.057 0.00971 3.723
Metro 30 2.256 0.0454 45.915
DEMetro_Z 2 5.516 4.5e-05 3.554
DEMetro_Z 5 5.673 0.000144 658.767
DEMetro_Z 10 8.842 2.49e-06 583.946
DEMetro_Z 15 10.080 6.79e-07 151.545
DEMetro_Z 30 16.754 3.54e-09 1334.969
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -3.772 0.00309 -1.089
Metro_vs_DEMetro_Z 1 -5.614 0.000157 -1.621
Metro_vs_DEMetro_Z 2 -8.401 4.09e-06 -2.425
Metro_vs_DEMetro_Z 3 -10.046 7.06e-07 -2.900
Metro_vs_DEMetro_Z 4 -14.982 1.15e-08 -4.325
DEMetro_Z_vs_SMC 0 5.689 0.00014 1.642
DEMetro_Z_vs_SMC 1 4.990 0.000409 1.440
DEMetro_Z_vs_SMC 2 4.238 0.00139 1.223
DEMetro_Z_vs_SMC 3 1.533 0.154 0.442
DEMetro_Z_vs_SMC 4 10.100 6.69e-07 2.916
HMC_vs_DEMetro_Z 0 -3.761 0.00315 -1.086
HMC_vs_DEMetro_Z 1 -5.618 0.000156 -1.622
HMC_vs_DEMetro_Z 2 -8.940 2.24e-06 -2.581
HMC_vs_DEMetro_Z 3 -10.279 5.61e-07 -2.967
HMC_vs_DEMetro_Z 4 -17.946 1.7e-09 -5.181
HMC_vs_Metro 0 -1.459 0.173 -0.421
HMC_vs_Metro 1 -0.116 0.91 -0.033
HMC_vs_Metro 2 -0.505 0.623 -0.146
HMC_vs_Metro 3 0.086 0.933 0.025
HMC_vs_Metro 4 0.517 0.616 0.149
HMC_vs_SMC 0 2.130 0.0566 0.615
HMC_vs_SMC 1 -8.888 2.37e-06 -2.566
HMC_vs_SMC 2 -20.188 4.83e-10 -5.828
HMC_vs_SMC 3 -41.086 2.16e-13 -11.861
HMC_vs_SMC 4 -10.062 6.95e-07 -2.905
Metro_vs_SMC 0 3.097 0.0102 0.894
Metro_vs_SMC 1 -9.698 1e-06 -2.799
Metro_vs_SMC 2 -24.813 5.23e-11 -7.163
Metro_vs_SMC 3 -33.336 2.11e-12 -9.623
Metro_vs_SMC 4 -22.204 1.74e-10 -6.410
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.156 0.122 0.038 0.902
HMC 5 0.194 0.113 0.015 5.310
HMC 10 0.296 0.110 0.013 14.158
HMC 15 0.283 0.131 0.039 3.882
HMC 30 1.006 0.111 0.012 73.364
SMC 2 0.134 0.122 0.038 0.328
SMC 5 1.330 0.113 0.015 79.507
SMC 10 3.955 0.110 0.013 291.834
SMC 15 5.120 0.131 0.039 127.591
SMC 30 6.784 0.111 0.012 546.646
Metro 2 0.183 0.122 0.038 1.611
Metro 5 0.197 0.113 0.015 5.485
Metro 10 0.332 0.110 0.013 16.898
Metro 15 0.277 0.131 0.039 3.723
Metro 30 0.671 0.111 0.012 45.915
DEMetro_Z 2 0.256 0.122 0.038 3.554
DEMetro_Z 5 10.202 0.113 0.015 658.767
DEMetro_Z 10 7.804 0.110 0.013 583.946
DEMetro_Z 15 6.056 0.131 0.039 151.545
DEMetro_Z 30 16.409 0.111 0.012 1334.969
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 1.934 0.0662 0.831
HMC 5 2.612 0.024 10.558
HMC 10 2.434 0.0331 17.961
HMC 15 3.034 0.0113 15.931
HMC 30 3.024 0.0116 82.178
SMC 2 1.648 0.118 0.985
SMC 5 20.420 3.82e-10 96.840
SMC 10 80.298 6.41e-17 205.177
SMC 15 93.490 7.66e-18 195.454
SMC 30 87.610 3.91e-17 357.325
Metro 2 5.302 6.45e-05 3.326
Metro 5 8.520 1.79e-06 10.967
Metro 10 5.988 8.63e-05 21.986
Metro 15 6.141 6.8e-05 19.603
Metro 30 6.462 4.64e-05 73.960
DEMetro_Z 2 5.822 6.24e-05 6.014
DEMetro_Z 5 14.209 1.99e-08 186.419
DEMetro_Z 10 30.408 5.47e-12 243.808
DEMetro_Z 15 31.611 3.51e-12 215.608
DEMetro_Z 30 49.074 2.93e-14 436.952
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 4.875 0.000491 1.407
DEMetro_Z_vs_SMC 1 6.751 3.15e-05 1.949
DEMetro_Z_vs_SMC 2 4.869 0.000495 1.406
DEMetro_Z_vs_SMC 3 2.879 0.015 0.831
DEMetro_Z_vs_SMC 4 8.516 3.59e-06 2.458
HMC_vs_Metro 0 -3.647 0.00384 -1.053
HMC_vs_Metro 1 -0.094 0.927 -0.027
HMC_vs_Metro 2 -0.658 0.524 -0.190
HMC_vs_Metro 3 -0.584 0.571 -0.168
HMC_vs_Metro 4 0.282 0.783 0.081
Metro_vs_DEMetro_Z 0 -2.031 0.0671 -0.586
Metro_vs_DEMetro_Z 1 -13.447 3.58e-08 -3.882
Metro_vs_DEMetro_Z 2 -20.516 4.07e-10 -5.923
Metro_vs_DEMetro_Z 3 -29.753 7.3e-12 -8.589
Metro_vs_DEMetro_Z 4 -28.660 1.1e-11 -8.273
HMC_vs_SMC 0 -0.321 0.754 -0.093
HMC_vs_SMC 1 -12.153 1.02e-07 -3.508
HMC_vs_SMC 2 -24.642 5.64e-11 -7.114
HMC_vs_SMC 3 -33.678 1.89e-12 -9.722
HMC_vs_SMC 4 -10.005 7.36e-07 -2.888
Metro_vs_SMC 0 3.420 0.00572 0.987
Metro_vs_SMC 1 -17.348 2.44e-09 -5.008
Metro_vs_SMC 2 -39.360 3.45e-13 -11.362
Metro_vs_SMC 3 -38.403 4.52e-13 -11.086
Metro_vs_SMC 4 -22.978 1.2e-10 -6.633
HMC_vs_DEMetro_Z 0 -4.978 0.000416 -1.437
HMC_vs_DEMetro_Z 1 -14.162 2.08e-08 -4.088
HMC_vs_DEMetro_Z 2 -18.766 1.06e-09 -5.417
HMC_vs_DEMetro_Z 3 -24.016 7.45e-11 -6.933
HMC_vs_DEMetro_Z 4 -14.089 2.2e-08 -4.067
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.018 0.014 0.004 0.831
HMC 5 0.038 0.014 0.002 10.558
HMC 10 0.048 0.015 0.002 17.961
HMC 15 0.046 0.015 0.002 15.931
HMC 30 0.103 0.015 0.001 82.178
SMC 2 0.019 0.014 0.004 0.985
SMC 5 0.231 0.014 0.002 96.840
SMC 10 0.399 0.015 0.002 205.177
SMC 15 0.399 0.015 0.002 195.454
SMC 30 0.396 0.015 0.001 357.325
Metro 2 0.029 0.014 0.004 3.326
Metro 5 0.038 0.014 0.002 10.967
Metro 10 0.056 0.015 0.002 21.986
Metro 15 0.054 0.015 0.002 19.603
Metro 30 0.094 0.015 0.001 73.960
DEMetro_Z 2 0.041 0.014 0.004 6.014
DEMetro_Z 5 0.432 0.014 0.002 186.419
DEMetro_Z 10 0.471 0.015 0.002 243.808
DEMetro_Z 15 0.439 0.015 0.002 215.608
DEMetro_Z 30 0.481 0.015 0.001 436.952
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -0.049 0.961 -0.019
HMC 5 2.227 0.037 1.031
HMC 10 0.468 0.645 0.257
HMC 15 1.057 0.312 2.057
HMC 30 1.120 0.286 41.637
SMC 2 -1.612 0.124 -0.540
SMC 5 5.131 0.000216 5.773
SMC 10 5.326 0.000237 25.388
SMC 15 6.545 2.74e-05 9.025
SMC 30 11.888 7.84e-08 21.803
Metro 2 2.258 0.0435 3.234
Metro 5 1.312 0.216 11.876
Metro 10 2.778 0.0176 6.756
Metro 15 3.640 0.00157 1.725
Metro 30 1.817 0.0966 28.405
DEMetro_Z 2 1.868 0.0818 1.395
DEMetro_Z 5 2.712 0.0202 79.137
DEMetro_Z 10 4.503 0.000896 109.078
DEMetro_Z 15 7.240 1.65e-05 67.475
DEMetro_Z 30 12.859 5.69e-08 672.567
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -1.700 0.117 -0.491
HMC_vs_DEMetro_Z 1 -2.672 0.0217 -0.771
HMC_vs_DEMetro_Z 2 -4.525 0.000864 -1.306
HMC_vs_DEMetro_Z 3 -8.224 5.02e-06 -2.374
HMC_vs_DEMetro_Z 4 -9.002 2.09e-06 -2.599
Metro_vs_SMC 0 2.675 0.0216 0.772
Metro_vs_SMC 1 0.673 0.515 0.194
Metro_vs_SMC 2 -3.768 0.00311 -1.088
Metro_vs_SMC 3 -5.525 0.000179 -1.595
Metro_vs_SMC 4 0.430 0.675 0.124
Metro_vs_DEMetro_Z 0 1.266 0.232 0.365
Metro_vs_DEMetro_Z 1 -2.081 0.0616 -0.601
Metro_vs_DEMetro_Z 2 -4.143 0.00164 -1.196
Metro_vs_DEMetro_Z 3 -7.012 2.23e-05 -2.024
Metro_vs_DEMetro_Z 4 -10.656 3.9e-07 -3.076
HMC_vs_Metro 0 -2.073 0.0625 -0.598
HMC_vs_Metro 1 -1.195 0.257 -0.345
HMC_vs_Metro 2 -2.499 0.0296 -0.721
HMC_vs_Metro 3 0.171 0.867 0.049
HMC_vs_Metro 4 0.313 0.76 0.090
HMC_vs_SMC 0 2.198 0.0503 0.634
HMC_vs_SMC 1 -4.785 0.000567 -1.381
HMC_vs_SMC 2 -5.080 0.000355 -1.466
HMC_vs_SMC 3 -6.759 3.12e-05 -1.951
HMC_vs_SMC 4 0.531 0.606 0.153
DEMetro_Z_vs_SMC 0 2.472 0.031 0.714
DEMetro_Z_vs_SMC 1 2.517 0.0286 0.727
DEMetro_Z_vs_SMC 2 3.265 0.00753 0.943
DEMetro_Z_vs_SMC 3 6.921 2.52e-05 1.998
DEMetro_Z_vs_SMC 4 12.426 8.12e-08 3.587
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.071 0.072 0.040 -0.019
HMC 5 0.077 0.053 0.023 1.031
HMC 10 0.068 0.065 0.015 0.257
HMC 15 0.139 0.073 0.032 2.057
HMC 30 0.406 0.066 0.008 41.637
SMC 2 0.050 0.072 0.040 -0.540
SMC 5 0.187 0.053 0.023 5.773
SMC 10 0.439 0.065 0.015 25.388
SMC 15 0.361 0.073 0.032 9.025
SMC 30 0.244 0.066 0.008 21.803
Metro 2 0.201 0.072 0.040 3.234
Metro 5 0.328 0.053 0.023 11.876
Metro 10 0.164 0.065 0.015 6.756
Metro 15 0.128 0.073 0.032 1.725
Metro 30 0.298 0.066 0.008 28.405
DEMetro_Z 2 0.128 0.072 0.040 1.395
DEMetro_Z 5 1.880 0.053 0.023 79.137
DEMetro_Z 10 1.671 0.065 0.015 109.078
DEMetro_Z 15 2.224 0.073 0.032 67.475
DEMetro_Z 30 5.566 0.066 0.008 672.567
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -0.094 0.926 -0.036
HMC 5 0.636 0.534 0.428
HMC 10 1.671 0.117 1.426
HMC 15 0.930 0.372 5.238
HMC 30 0.995 0.341 12.800
SMC 2 -0.147 0.884 -0.057
SMC 5 1.407 0.175 0.700
SMC 10 5.983 6.97e-05 9.513
SMC 15 4.505 0.000417 1.418
SMC 30 27.495 8.28e-13 28.326
Metro 2 0.268 0.792 0.102
Metro 5 0.992 0.342 3.461
Metro 10 1.739 0.109 4.101
Metro 15 -1.452 0.173 -0.424
Metro 30 1.095 0.296 4.018
DEMetro_Z 2 -0.008 0.994 -0.003
DEMetro_Z 5 1.678 0.121 63.429
DEMetro_Z 10 1.856 0.0904 33.956
DEMetro_Z 15 2.316 0.0385 2.784
DEMetro_Z 30 6.910 2.52e-05 57.595
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.565 0.583 0.163
HMC_vs_SMC 1 -0.409 0.69 -0.118
HMC_vs_SMC 2 -4.123 0.00169 -1.190
HMC_vs_SMC 3 0.684 0.508 0.197
HMC_vs_SMC 4 -1.226 0.246 -0.354
Metro_vs_DEMetro_Z 0 1.055 0.314 0.305
Metro_vs_DEMetro_Z 1 -1.556 0.148 -0.449
Metro_vs_DEMetro_Z 2 -1.583 0.142 -0.457
Metro_vs_DEMetro_Z 3 -2.745 0.0191 -0.792
Metro_vs_DEMetro_Z 4 -5.132 0.000327 -1.481
HMC_vs_Metro 0 -1.666 0.124 -0.481
HMC_vs_Metro 1 -0.831 0.424 -0.240
HMC_vs_Metro 2 -1.085 0.301 -0.313
HMC_vs_Metro 3 1.007 0.336 0.291
HMC_vs_Metro 4 0.643 0.533 0.186
HMC_vs_DEMetro_Z 0 -0.806 0.438 -0.233
HMC_vs_DEMetro_Z 1 -1.677 0.122 -0.484
HMC_vs_DEMetro_Z 2 -1.780 0.103 -0.514
HMC_vs_DEMetro_Z 3 0.499 0.627 0.144
HMC_vs_DEMetro_Z 4 -2.692 0.021 -0.777
Metro_vs_SMC 0 1.685 0.12 0.487
Metro_vs_SMC 1 0.801 0.44 0.231
Metro_vs_SMC 2 -2.458 0.0318 -0.709
Metro_vs_SMC 3 -15.320 9.12e-09 -4.422
Metro_vs_SMC 4 -6.434 4.85e-05 -1.857
DEMetro_Z_vs_SMC 0 1.788 0.101 0.516
DEMetro_Z_vs_SMC 1 1.671 0.123 0.482
DEMetro_Z_vs_SMC 2 1.294 0.222 0.374
DEMetro_Z_vs_SMC 3 1.169 0.267 0.337
DEMetro_Z_vs_SMC 4 3.587 0.00427 1.035
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 8.229 8.779 15.112 -0.036
HMC 5 7.288 5.105 5.103 0.428
HMC 10 8.613 3.930 3.285 1.426
HMC 15 184.784 17.964 31.848 5.238
HMC 30 51.365 4.774 3.640 12.800
SMC 2 7.911 8.779 15.112 -0.057
SMC 5 8.675 5.105 5.103 0.700
SMC 10 35.178 3.930 3.285 9.513
SMC 15 63.136 17.964 31.848 1.418
SMC 30 107.877 4.774 3.640 28.326
Metro 2 10.328 8.779 15.112 0.102
Metro 5 22.769 5.105 5.103 3.461
Metro 10 17.401 3.930 3.285 4.101
Metro 15 4.464 17.964 31.848 -0.424
Metro 30 19.400 4.774 3.640 4.018
DEMetro_Z 2 8.731 8.779 15.112 -0.003
DEMetro_Z 5 328.793 5.105 5.103 63.429
DEMetro_Z 10 115.466 3.930 3.285 33.956
DEMetro_Z 15 106.630 17.964 31.848 2.784
DEMetro_Z 30 214.412 4.774 3.640 57.595
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.323 0.0301 0.878
HMC 5 1.968 0.074 4.678
HMC 10 3.218 0.00774 6.077
HMC 15 1.236 0.242 20.140
HMC 30 1.928 0.0801 47.470
SMC 2 0.246 0.808 0.112
SMC 5 5.312 0.000247 56.418
SMC 10 11.914 1.25e-07 229.026
SMC 15 24.403 5.56e-11 119.339
SMC 30 53.436 1.17e-14 559.479
Metro 2 2.903 0.0133 4.111
Metro 5 1.730 0.111 23.165
Metro 10 1.729 0.112 46.640
Metro 15 4.692 0.000185 2.658
Metro 30 1.604 0.137 68.286
DEMetro_Z 2 5.761 2.23e-05 3.438
DEMetro_Z 5 2.275 0.0439 288.225
DEMetro_Z 10 3.501 0.00496 300.782
DEMetro_Z 15 6.392 5.13e-05 137.818
DEMetro_Z 30 14.310 1.87e-08 815.183
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 0.432 0.674 0.125
Metro_vs_DEMetro_Z 1 -2.028 0.0675 -0.585
Metro_vs_DEMetro_Z 2 -2.693 0.0209 -0.777
Metro_vs_DEMetro_Z 3 -6.271 6.08e-05 -1.810
Metro_vs_DEMetro_Z 4 -8.602 3.26e-06 -2.483
DEMetro_Z_vs_SMC 0 6.504 4.4e-05 1.878
DEMetro_Z_vs_SMC 1 1.900 0.0839 0.549
DEMetro_Z_vs_SMC 2 0.741 0.474 0.214
DEMetro_Z_vs_SMC 3 0.831 0.424 0.240
DEMetro_Z_vs_SMC 4 4.721 0.000628 1.363
HMC_vs_DEMetro_Z 0 -6.247 6.28e-05 -1.803
HMC_vs_DEMetro_Z 1 -2.245 0.0463 -0.648
HMC_vs_DEMetro_Z 2 -3.448 0.00544 -0.995
HMC_vs_DEMetro_Z 3 -5.854 0.00011 -1.690
HMC_vs_DEMetro_Z 4 -11.973 1.19e-07 -3.456
HMC_vs_Metro 0 -2.195 0.0506 -0.634
HMC_vs_Metro 1 -1.303 0.219 -0.376
HMC_vs_Metro 2 -1.468 0.17 -0.424
HMC_vs_Metro 3 1.066 0.309 0.308
HMC_vs_Metro 4 -0.433 0.673 -0.125
HMC_vs_SMC 0 1.904 0.0833 0.550
HMC_vs_SMC 1 -4.846 0.000514 -1.399
HMC_vs_SMC 2 -10.709 3.71e-07 -3.091
HMC_vs_SMC 3 -6.217 6.56e-05 -1.795
HMC_vs_SMC 4 -19.649 6.46e-10 -5.672
Metro_vs_SMC 0 3.022 0.0116 0.872
Metro_vs_SMC 1 -2.015 0.069 -0.582
Metro_vs_SMC 2 -6.669 3.52e-05 -1.925
Metro_vs_SMC 3 -23.081 1.14e-10 -6.663
Metro_vs_SMC 4 -11.185 2.39e-07 -3.229
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.155 0.122 0.038 0.878
HMC 5 0.184 0.113 0.015 4.678
HMC 10 0.190 0.110 0.013 6.077
HMC 15 0.919 0.131 0.039 20.140
HMC 30 0.690 0.111 0.012 47.470
SMC 2 0.126 0.122 0.038 0.112
SMC 5 0.977 0.113 0.015 56.418
SMC 10 3.127 0.110 0.013 229.026
SMC 15 4.797 0.131 0.039 119.339
SMC 30 6.941 0.111 0.012 559.479
Metro 2 0.277 0.122 0.038 4.111
Metro 5 0.467 0.113 0.015 23.165
Metro 10 0.724 0.110 0.013 46.640
Metro 15 0.235 0.131 0.039 2.658
Metro 30 0.944 0.111 0.012 68.286
DEMetro_Z 2 0.252 0.122 0.038 3.438
DEMetro_Z 5 4.527 0.113 0.015 288.225
DEMetro_Z 10 4.073 0.110 0.013 300.782
DEMetro_Z 15 5.519 0.131 0.039 137.818
DEMetro_Z 30 10.063 0.111 0.012 815.183
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.821 0.0108 1.464
HMC 5 2.660 0.021 3.910
HMC 10 3.393 0.00567 6.776
HMC 15 1.663 0.125 45.702
HMC 30 1.491 0.164 94.461
SMC 2 1.066 0.298 0.430
SMC 5 8.612 3.18e-06 78.216
SMC 10 30.707 4.72e-12 183.841
SMC 15 65.692 7.54e-16 197.930
SMC 30 109.737 2.68e-18 361.030
Metro 2 3.972 0.00146 3.470
Metro 5 5.067 0.000335 13.032
Metro 10 2.407 0.0348 40.912
Metro 15 5.701 0.000127 15.900
Metro 30 3.482 0.00513 93.183
DEMetro_Z 2 5.634 6.15e-05 4.648
DEMetro_Z 5 4.050 0.00192 95.843
DEMetro_Z 10 11.356 2.04e-07 210.000
DEMetro_Z 15 18.313 1.35e-09 233.670
DEMetro_Z 30 40.536 2.44e-13 493.180
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 4.656 0.000698 1.344
DEMetro_Z_vs_SMC 1 0.704 0.496 0.203
DEMetro_Z_vs_SMC 2 1.273 0.229 0.367
DEMetro_Z_vs_SMC 3 2.835 0.0162 0.818
DEMetro_Z_vs_SMC 4 11.051 2.7e-07 3.190
HMC_vs_Metro 0 -1.994 0.0715 -0.576
HMC_vs_Metro 1 -2.700 0.0207 -0.779
HMC_vs_Metro 2 -1.961 0.0757 -0.566
HMC_vs_Metro 3 1.048 0.317 0.303
HMC_vs_Metro 4 0.019 0.985 0.005
Metro_vs_DEMetro_Z 0 -1.082 0.302 -0.312
Metro_vs_DEMetro_Z 1 -3.257 0.00765 -0.940
Metro_vs_DEMetro_Z 2 -6.188 6.83e-05 -1.786
Metro_vs_DEMetro_Z 3 -17.412 2.35e-09 -5.026
Metro_vs_DEMetro_Z 4 -13.006 5.07e-08 -3.754
HMC_vs_SMC 0 1.768 0.105 0.510
HMC_vs_SMC 1 -8.235 4.96e-06 -2.377
HMC_vs_SMC 2 -24.045 7.35e-11 -6.941
HMC_vs_SMC 3 -5.936 9.78e-05 -1.714
HMC_vs_SMC 4 -4.139 0.00165 -1.195
Metro_vs_SMC 0 3.750 0.00321 1.083
Metro_vs_SMC 1 -7.319 1.51e-05 -2.113
Metro_vs_SMC 2 -8.592 3.29e-06 -2.480
Metro_vs_SMC 3 -37.942 5.15e-13 -10.953
Metro_vs_SMC 4 -10.177 6.2e-07 -2.938
HMC_vs_DEMetro_Z 0 -4.266 0.00133 -1.232
HMC_vs_DEMetro_Z 1 -3.864 0.00263 -1.116
HMC_vs_DEMetro_Z 2 -10.650 3.93e-07 -3.074
HMC_vs_DEMetro_Z 3 -6.819 2.88e-05 -1.968
HMC_vs_DEMetro_Z 4 -5.897 0.000104 -1.702
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.021 0.014 0.004 1.464
HMC 5 0.023 0.014 0.002 3.910
HMC 10 0.027 0.015 0.002 6.776
HMC 15 0.105 0.015 0.002 45.702
HMC 30 0.116 0.015 0.001 94.461
SMC 2 0.016 0.014 0.004 0.430
SMC 5 0.189 0.014 0.002 78.216
SMC 10 0.359 0.015 0.002 183.841
SMC 15 0.404 0.015 0.002 197.930
SMC 30 0.400 0.015 0.001 361.030
Metro 2 0.030 0.014 0.004 3.470
Metro 5 0.043 0.014 0.002 13.032
Metro 10 0.091 0.015 0.002 40.912
Metro 15 0.046 0.015 0.002 15.900
Metro 30 0.114 0.015 0.001 93.183
DEMetro_Z 2 0.035 0.014 0.004 4.648
DEMetro_Z 5 0.229 0.014 0.002 95.843
DEMetro_Z 10 0.408 0.015 0.002 210.000
DEMetro_Z 15 0.474 0.015 0.002 233.670
DEMetro_Z 30 0.541 0.015 0.001 493.180
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
2 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
30 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
30 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2
5
10
15
30
Chain
2
5
10
15
30

Vary_Dimension_with_high_Multimodality (Mixture, dimension, 12 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 5.562 0.000167 37.881
HMC 5 4.958 0.000427 44.824
HMC 10 4.037 0.00195 39.000
HMC 15 2.944 0.0133 27.382
HMC 30 3.871 0.00259 36.281
SMC 2 1.308 0.209 0.428
SMC 5 -0.281 0.781 -0.100
SMC 10 0.039 0.969 0.019
SMC 15 -0.206 0.839 -0.072
SMC 30 0.207 0.838 0.084
Metro 2 3.929 0.00234 27.906
Metro 5 3.295 0.00713 36.863
Metro 10 5.658 0.000145 35.901
Metro 15 4.112 0.00171 27.857
Metro 30 3.742 0.00324 31.482
DEMetro_Z 2 5.620 0.000153 32.678
DEMetro_Z 5 7.251 1.64e-05 105.668
DEMetro_Z 10 11.875 1.29e-07 300.941
DEMetro_Z 15 21.980 1.92e-10 358.927
DEMetro_Z 30 30.726 5.08e-12 529.976
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 0.543 0.598 0.157
HMC_vs_DEMetro_Z 1 -3.001 0.0121 -0.866
HMC_vs_DEMetro_Z 2 -9.738 9.63e-07 -2.811
HMC_vs_DEMetro_Z 3 -19.893 5.66e-10 -5.743
HMC_vs_DEMetro_Z 4 -27.201 1.93e-11 -7.852
Metro_vs_SMC 0 3.861 0.00265 1.115
Metro_vs_SMC 1 3.301 0.00707 0.953
Metro_vs_SMC 2 5.662 0.000146 1.634
Metro_vs_SMC 3 4.192 0.00151 1.210
Metro_vs_SMC 4 3.757 0.00317 1.085
Metro_vs_DEMetro_Z 0 -0.481 0.64 -0.139
Metro_vs_DEMetro_Z 1 -3.252 0.00771 -0.939
Metro_vs_DEMetro_Z 2 -10.545 4.34e-07 -3.044
Metro_vs_DEMetro_Z 3 -18.875 9.94e-10 -5.449
Metro_vs_DEMetro_Z 4 -27.077 2.03e-11 -7.816
HMC_vs_Metro 0 2.321 0.0405 0.670
HMC_vs_Metro 1 0.756 0.466 0.218
HMC_vs_Metro 2 0.347 0.735 0.100
HMC_vs_Metro 3 -0.040 0.969 -0.011
HMC_vs_Metro 4 1.568 0.145 0.453
HMC_vs_SMC 0 5.510 0.000183 1.591
HMC_vs_SMC 1 4.953 0.000434 1.430
HMC_vs_SMC 2 4.064 0.00187 1.173
HMC_vs_SMC 3 2.932 0.0136 0.846
HMC_vs_SMC 4 3.890 0.00252 1.123
DEMetro_Z_vs_SMC 0 5.577 0.000166 1.610
DEMetro_Z_vs_SMC 1 7.247 1.65e-05 2.092
DEMetro_Z_vs_SMC 2 11.851 1.32e-07 3.421
DEMetro_Z_vs_SMC 3 21.999 1.92e-10 6.350
DEMetro_Z_vs_SMC 4 30.598 5.38e-12 8.833
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 2.280 0.095 0.058 37.881
HMC 5 1.132 0.042 0.024 44.824
HMC 10 0.717 0.039 0.017 39.000
HMC 15 0.467 0.034 0.016 27.382
HMC 30 0.466 0.034 0.012 36.281
SMC 2 0.120 0.095 0.058 0.428
SMC 5 0.039 0.042 0.024 -0.100
SMC 10 0.039 0.039 0.017 0.019
SMC 15 0.033 0.034 0.016 -0.072
SMC 30 0.035 0.034 0.012 0.084
Metro 2 1.704 0.095 0.058 27.906
Metro 5 0.939 0.042 0.024 36.863
Metro 10 0.663 0.039 0.017 35.901
Metro 15 0.475 0.034 0.016 27.857
Metro 30 0.408 0.034 0.012 31.482
DEMetro_Z 2 1.980 0.095 0.058 32.678
DEMetro_Z 5 2.613 0.042 0.024 105.668
DEMetro_Z 10 5.272 0.039 0.017 300.941
DEMetro_Z 15 5.708 0.034 0.016 358.927
DEMetro_Z 30 6.343 0.034 0.012 529.976
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.631 0.00395 72.487
HMC 5 3.279 0.00735 79.857
HMC 10 2.898 0.0145 53.338
HMC 15 2.269 0.0444 93.577
HMC 30 2.865 0.0154 118.048
SMC 2 0.448 0.659 0.185
SMC 5 1.320 0.203 0.699
SMC 10 1.224 0.236 0.645
SMC 15 1.055 0.307 0.672
SMC 30 1.416 0.177 1.027
Metro 2 2.722 0.0199 51.092
Metro 5 2.434 0.0332 75.186
Metro 10 5.400 0.000214 38.220
Metro 15 3.973 0.00218 71.717
Metro 30 2.726 0.0197 93.961
DEMetro_Z 2 3.246 0.00779 50.136
DEMetro_Z 5 8.060 6.08e-06 792.552
DEMetro_Z 10 12.795 6e-08 2385.081
DEMetro_Z 15 11.806 1.38e-07 7355.687
DEMetro_Z 30 24.527 5.93e-11 10924.805
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 3.652 0.00381 1.054
HMC_vs_SMC 1 3.261 0.00758 0.941
HMC_vs_SMC 2 2.887 0.0148 0.833
HMC_vs_SMC 3 2.274 0.044 0.656
HMC_vs_SMC 4 2.826 0.0165 0.816
Metro_vs_DEMetro_Z 0 0.039 0.97 0.011
Metro_vs_DEMetro_Z 1 -6.453 4.72e-05 -1.863
Metro_vs_DEMetro_Z 2 -12.544 7.36e-08 -3.621
Metro_vs_DEMetro_Z 3 -11.841 1.33e-07 -3.418
Metro_vs_DEMetro_Z 4 -25.011 4.8e-11 -7.220
HMC_vs_Metro 0 1.812 0.0973 0.523
HMC_vs_Metro 1 0.174 0.865 0.050
HMC_vs_Metro 2 0.842 0.418 0.243
HMC_vs_Metro 3 0.477 0.643 0.138
HMC_vs_Metro 4 1.469 0.17 0.424
HMC_vs_DEMetro_Z 0 0.834 0.422 0.241
HMC_vs_DEMetro_Z 1 -6.556 4.1e-05 -1.892
HMC_vs_DEMetro_Z 2 -12.635 6.84e-08 -3.647
HMC_vs_DEMetro_Z 3 -11.653 1.57e-07 -3.364
HMC_vs_DEMetro_Z 4 -24.936 4.96e-11 -7.198
Metro_vs_SMC 0 2.738 0.0193 0.790
Metro_vs_SMC 1 2.406 0.0349 0.694
Metro_vs_SMC 2 5.242 0.000276 1.513
Metro_vs_SMC 3 3.882 0.00256 1.121
Metro_vs_SMC 4 2.682 0.0213 0.774
DEMetro_Z_vs_SMC 0 3.224 0.00811 0.931
DEMetro_Z_vs_SMC 1 8.033 6.28e-06 2.319
DEMetro_Z_vs_SMC 2 12.812 5.92e-08 3.699
DEMetro_Z_vs_SMC 3 11.804 1.38e-07 3.408
DEMetro_Z_vs_SMC 4 24.513 5.97e-11 7.076
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 10.111 0.155 0.137 72.487
HMC 5 4.029 0.076 0.049 79.857
HMC 10 2.612 0.072 0.048 53.338
HMC 15 1.776 0.049 0.018 93.577
HMC 30 1.932 0.045 0.016 118.048
SMC 2 0.181 0.155 0.137 0.185
SMC 5 0.111 0.076 0.049 0.699
SMC 10 0.102 0.072 0.048 0.645
SMC 15 0.062 0.049 0.018 0.672
SMC 30 0.062 0.045 0.016 1.027
Metro 2 7.172 0.155 0.137 51.092
Metro 5 3.798 0.076 0.049 75.186
Metro 10 1.892 0.072 0.048 38.220
Metro 15 1.373 0.049 0.018 71.717
Metro 30 1.547 0.045 0.016 93.961
DEMetro_Z 2 7.041 0.155 0.137 50.136
DEMetro_Z 5 39.304 0.076 0.049 792.552
DEMetro_Z 10 113.685 0.072 0.048 2385.081
DEMetro_Z 15 135.775 0.049 0.018 7355.687
DEMetro_Z 30 174.604 0.045 0.016 10924.805
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 5.550 0.000171 44.342
HMC 5 4.639 0.000716 55.077
HMC 10 4.134 0.00166 46.634
HMC 15 3.032 0.0114 33.803
HMC 30 3.935 0.00233 51.009
SMC 2 1.233 0.233 0.420
SMC 5 0.043 0.966 0.015
SMC 10 0.013 0.99 0.006
SMC 15 -0.119 0.907 -0.042
SMC 30 0.499 0.623 0.209
Metro 2 3.983 0.00214 31.010
Metro 5 3.382 0.00611 42.894
Metro 10 5.684 0.00014 43.846
Metro 15 4.142 0.00163 32.264
Metro 30 3.744 0.00324 44.373
DEMetro_Z 2 5.826 0.000113 39.832
DEMetro_Z 5 10.917 3.04e-07 205.510
DEMetro_Z 10 20.093 5.07e-10 640.960
DEMetro_Z 15 23.250 1.05e-10 800.436
DEMetro_Z 30 47.094 4.83e-14 1513.216
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -0.792 0.445 -0.229
Metro_vs_DEMetro_Z 1 -6.524 4.29e-05 -1.883
Metro_vs_DEMetro_Z 2 -18.466 1.26e-09 -5.331
Metro_vs_DEMetro_Z 3 -24.502 5.99e-11 -7.073
Metro_vs_DEMetro_Z 4 -51.866 1.68e-14 -14.972
DEMetro_Z_vs_SMC 0 5.804 0.000119 1.676
DEMetro_Z_vs_SMC 1 10.896 3.12e-07 3.145
DEMetro_Z_vs_SMC 2 20.112 5.03e-10 5.806
DEMetro_Z_vs_SMC 3 23.315 1.03e-10 6.730
DEMetro_Z_vs_SMC 4 46.912 5.06e-14 13.542
HMC_vs_DEMetro_Z 0 0.397 0.699 0.115
HMC_vs_DEMetro_Z 1 -5.730 0.000132 -1.654
HMC_vs_DEMetro_Z 2 -18.681 1.11e-09 -5.393
HMC_vs_DEMetro_Z 3 -21.232 2.81e-10 -6.129
HMC_vs_DEMetro_Z 4 -50.336 2.34e-14 -14.531
HMC_vs_Metro 0 2.921 0.0139 0.843
HMC_vs_Metro 1 1.014 0.333 0.293
HMC_vs_Metro 2 0.253 0.805 0.073
HMC_vs_Metro 3 0.108 0.916 0.031
HMC_vs_Metro 4 1.681 0.121 0.485
HMC_vs_SMC 0 5.512 0.000183 1.591
HMC_vs_SMC 1 4.654 0.000701 1.343
HMC_vs_SMC 2 4.162 0.00159 1.201
HMC_vs_SMC 3 3.019 0.0117 0.871
HMC_vs_SMC 4 3.933 0.00234 1.135
Metro_vs_SMC 0 3.923 0.00238 1.132
Metro_vs_SMC 1 3.374 0.00621 0.974
Metro_vs_SMC 2 5.663 0.000146 1.635
Metro_vs_SMC 3 4.216 0.00145 1.217
Metro_vs_SMC 4 3.743 0.00325 1.081
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 2.073 0.103 0.044 44.342
HMC 5 0.968 0.051 0.017 55.077
HMC 10 0.592 0.047 0.012 46.634
HMC 15 0.396 0.042 0.010 33.803
HMC 30 0.375 0.040 0.007 51.009
SMC 2 0.121 0.103 0.044 0.420
SMC 5 0.051 0.051 0.017 0.015
SMC 10 0.047 0.047 0.012 0.006
SMC 15 0.042 0.042 0.010 -0.042
SMC 30 0.041 0.040 0.007 0.209
Metro 2 1.481 0.103 0.044 31.010
Metro 5 0.765 0.051 0.017 42.894
Metro 10 0.560 0.047 0.012 43.846
Metro 15 0.380 0.042 0.010 32.264
Metro 30 0.332 0.040 0.007 44.373
DEMetro_Z 2 1.873 0.103 0.044 39.832
DEMetro_Z 5 3.473 0.051 0.017 205.510
DEMetro_Z 10 7.536 0.047 0.012 640.960
DEMetro_Z 15 8.424 0.042 0.010 800.436
DEMetro_Z 30 9.988 0.040 0.007 1513.216
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 5.687 0.00014 46.414
HMC 5 5.057 0.000366 57.530
HMC 10 3.992 0.00211 44.174
HMC 15 2.999 0.0121 33.721
HMC 30 3.831 0.00278 42.315
SMC 2 1.388 0.182 0.472
SMC 5 0.165 0.871 0.059
SMC 10 0.050 0.961 0.023
SMC 15 0.065 0.949 0.023
SMC 30 0.581 0.567 0.229
Metro 2 4.144 0.00162 34.573
Metro 5 3.313 0.00691 47.884
Metro 10 5.740 0.000129 40.348
Metro 15 4.136 0.00165 35.423
Metro 30 3.655 0.00378 35.644
DEMetro_Z 2 5.760 0.000125 40.101
DEMetro_Z 5 16.837 3.14e-09 96.979
DEMetro_Z 10 34.443 1.12e-12 120.856
DEMetro_Z 15 59.514 1.53e-15 133.908
DEMetro_Z 30 49.086 1.68e-14 128.307
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 5.730 0.000132 1.654
DEMetro_Z_vs_SMC 1 16.759 3.53e-09 4.838
DEMetro_Z_vs_SMC 2 33.508 2e-12 9.673
DEMetro_Z_vs_SMC 3 58.125 4.83e-15 16.779
DEMetro_Z_vs_SMC 4 48.162 3.79e-14 13.903
HMC_vs_Metro 0 2.383 0.0363 0.688
HMC_vs_Metro 1 0.687 0.506 0.198
HMC_vs_Metro 2 0.376 0.714 0.108
HMC_vs_Metro 3 -0.115 0.91 -0.033
HMC_vs_Metro 4 1.748 0.108 0.505
Metro_vs_DEMetro_Z 0 -0.465 0.651 -0.134
Metro_vs_DEMetro_Z 1 -2.829 0.0164 -0.817
Metro_vs_DEMetro_Z 2 -12.073 1.09e-07 -3.485
Metro_vs_DEMetro_Z 3 -10.946 2.98e-07 -3.160
Metro_vs_DEMetro_Z 4 -8.204 5.14e-06 -2.368
HMC_vs_SMC 0 5.620 0.000156 1.622
HMC_vs_SMC 1 5.052 0.000371 1.458
HMC_vs_SMC 2 4.012 0.00204 1.158
HMC_vs_SMC 3 2.977 0.0126 0.859
HMC_vs_SMC 4 3.836 0.00277 1.107
Metro_vs_SMC 0 4.072 0.00185 1.175
Metro_vs_SMC 1 3.299 0.00709 0.952
Metro_vs_SMC 2 5.733 0.000132 1.655
Metro_vs_SMC 3 4.198 0.00149 1.212
Metro_vs_SMC 4 3.652 0.00381 1.054
HMC_vs_DEMetro_Z 0 0.547 0.595 0.158
HMC_vs_DEMetro_Z 1 -2.639 0.023 -0.762
HMC_vs_DEMetro_Z 2 -7.204 1.74e-05 -2.080
HMC_vs_DEMetro_Z 3 -9.154 1.77e-06 -2.643
HMC_vs_DEMetro_Z 4 -6.907 2.56e-05 -1.994
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.344 0.014 0.007 46.414
HMC 5 0.256 0.010 0.004 57.530
HMC 10 0.216 0.012 0.005 44.174
HMC 15 0.157 0.012 0.004 33.721
HMC 30 0.195 0.015 0.004 42.315
SMC 2 0.017 0.014 0.007 0.472
SMC 5 0.010 0.010 0.004 0.059
SMC 10 0.012 0.012 0.005 0.023
SMC 15 0.012 0.012 0.004 0.023
SMC 30 0.016 0.015 0.004 0.229
Metro 2 0.260 0.014 0.007 34.573
Metro 5 0.214 0.010 0.004 47.884
Metro 10 0.198 0.012 0.005 40.348
Metro 15 0.164 0.012 0.004 35.423
Metro 30 0.167 0.015 0.004 35.644
DEMetro_Z 2 0.299 0.014 0.007 40.101
DEMetro_Z 5 0.424 0.010 0.004 96.979
DEMetro_Z 10 0.569 0.012 0.005 120.856
DEMetro_Z 15 0.586 0.012 0.004 133.908
DEMetro_Z 30 0.562 0.015 0.004 128.307
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 163.377 6.13e-35 71.511
HMC 5 230.797 8.07e-37 108.686
HMC 10 202.744 3.18e-33 106.303
HMC 15 223.306 3.82e-38 95.636
HMC 30 187.937 8.89e-35 89.332
SMC 2 -1.177 0.252 -0.450
SMC 5 0.903 0.376 0.363
SMC 10 0.279 0.783 0.120
SMC 15 0.211 0.835 0.107
SMC 30 -1.069 0.299 -0.359
Metro 2 11.532 1.67e-07 65.765
Metro 5 225.837 4.02e-36 108.774
Metro 10 27.968 1.13e-11 101.457
Metro 15 8.017 6.33e-06 78.121
Metro 30 15.431 7.88e-09 83.880
DEMetro_Z 2 7.909 7.14e-06 59.034
DEMetro_Z 5 9.874 8.31e-07 120.739
DEMetro_Z 10 10.533 4.39e-07 529.331
DEMetro_Z 15 13.750 2.83e-08 587.025
DEMetro_Z 30 15.001 1.14e-08 916.835
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 1.643 0.129 0.474
HMC_vs_DEMetro_Z 1 -0.970 0.353 -0.280
HMC_vs_DEMetro_Z 2 -8.431 3.95e-06 -2.434
HMC_vs_DEMetro_Z 3 -11.518 1.77e-07 -3.325
HMC_vs_DEMetro_Z 4 -13.554 3.3e-08 -3.913
Metro_vs_SMC 0 11.517 1.77e-07 3.325
Metro_vs_SMC 1 182.977 1.63e-20 52.821
Metro_vs_SMC 2 28.360 1.23e-11 8.187
Metro_vs_SMC 3 8.080 5.94e-06 2.332
Metro_vs_SMC 4 15.248 9.59e-09 4.402
Metro_vs_DEMetro_Z 0 0.665 0.52 0.192
Metro_vs_DEMetro_Z 1 -0.958 0.359 -0.277
Metro_vs_DEMetro_Z 2 -8.477 3.75e-06 -2.447
Metro_vs_DEMetro_Z 3 -10.568 4.25e-07 -3.051
Metro_vs_DEMetro_Z 4 -13.351 3.86e-08 -3.854
HMC_vs_Metro 0 1.037 0.322 0.299
HMC_vs_Metro 1 -0.534 0.604 -0.154
HMC_vs_Metro 2 1.272 0.23 0.367
HMC_vs_Metro 3 1.803 0.0988 0.521
HMC_vs_Metro 4 0.998 0.34 0.288
HMC_vs_SMC 0 164.528 5.24e-20 47.495
HMC_vs_SMC 1 207.793 4.02e-21 59.985
HMC_vs_SMC 2 187.010 1.28e-20 53.985
HMC_vs_SMC 3 188.932 1.15e-20 54.540
HMC_vs_SMC 4 243.228 7.12e-22 70.214
DEMetro_Z_vs_SMC 0 7.966 6.8e-06 2.300
DEMetro_Z_vs_SMC 1 9.944 7.82e-07 2.871
DEMetro_Z_vs_SMC 2 10.522 4.44e-07 3.037
DEMetro_Z_vs_SMC 3 13.755 2.83e-08 3.971
DEMetro_Z_vs_SMC 4 15.011 1.13e-08 4.333
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 4.219 0.095 0.058 71.511
HMC 5 2.686 0.042 0.024 108.686
HMC 10 1.887 0.039 0.017 106.303
HMC 15 1.546 0.034 0.016 95.636
HMC 30 1.097 0.034 0.012 89.332
SMC 2 0.069 0.095 0.058 -0.450
SMC 5 0.051 0.042 0.024 0.363
SMC 10 0.041 0.039 0.017 0.120
SMC 15 0.036 0.034 0.016 0.107
SMC 30 0.029 0.034 0.012 -0.359
Metro 2 3.888 0.095 0.058 65.765
Metro 5 2.688 0.042 0.024 108.774
Metro 10 1.803 0.039 0.017 101.457
Metro 15 1.269 0.034 0.016 78.121
Metro 30 1.032 0.034 0.012 83.880
DEMetro_Z 2 3.500 0.095 0.058 59.034
DEMetro_Z 5 2.979 0.042 0.024 120.739
DEMetro_Z 10 9.243 0.039 0.017 529.331
DEMetro_Z 15 9.314 0.034 0.016 587.025
DEMetro_Z 30 10.949 0.034 0.012 916.835
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 481.407 5.24e-45 184.234
HMC 5 622.718 7.41e-43 322.788
HMC 10 426.026 8.57e-38 236.513
HMC 15 501.323 3.31e-29 502.037
HMC 30 568.515 4.16e-34 407.950
SMC 2 -0.722 0.479 -0.244
SMC 5 1.369 0.187 0.742
SMC 10 0.952 0.352 0.447
SMC 15 1.409 0.175 0.765
SMC 30 0.935 0.361 0.468
Metro 2 11.021 2.76e-07 168.967
Metro 5 567.035 2.47e-39 322.892
Metro 10 16.091 5.37e-09 217.214
Metro 15 6.926 2.5e-05 390.802
Metro 30 12.014 1.15e-07 376.857
DEMetro_Z 2 6.992 2.29e-05 146.368
DEMetro_Z 5 6.601 3.86e-05 375.216
DEMetro_Z 10 7.519 1.17e-05 653.238
DEMetro_Z 15 9.298 1.52e-06 1222.827
DEMetro_Z 30 11.250 2.25e-07 1195.056
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 504.010 2.36e-25 145.495
HMC_vs_SMC 1 422.811 1.63e-24 122.055
HMC_vs_SMC 2 291.200 9.83e-23 84.062
HMC_vs_SMC 3 560.746 7.29e-26 161.873
HMC_vs_SMC 4 491.438 3.11e-25 141.866
Metro_vs_DEMetro_Z 0 0.810 0.435 0.234
Metro_vs_DEMetro_Z 1 -0.918 0.378 -0.265
Metro_vs_DEMetro_Z 2 -5.203 0.000293 -1.502
Metro_vs_DEMetro_Z 3 -5.993 9.02e-05 -1.730
Metro_vs_DEMetro_Z 4 -7.751 8.81e-06 -2.237
HMC_vs_Metro 0 1.003 0.337 0.290
HMC_vs_Metro 1 -0.692 0.503 -0.200
HMC_vs_Metro 2 1.430 0.18 0.413
HMC_vs_Metro 3 1.960 0.0759 0.566
HMC_vs_Metro 4 0.992 0.343 0.286
HMC_vs_DEMetro_Z 0 1.802 0.099 0.520
HMC_vs_DEMetro_Z 1 -0.920 0.377 -0.266
HMC_vs_DEMetro_Z 2 -4.799 0.000555 -1.385
HMC_vs_DEMetro_Z 3 -5.475 0.000193 -1.580
HMC_vs_DEMetro_Z 4 -7.421 1.32e-05 -2.142
Metro_vs_SMC 0 10.994 2.85e-07 3.174
Metro_vs_SMC 1 398.993 3.08e-24 115.179
Metro_vs_SMC 2 15.996 5.78e-09 4.618
Metro_vs_SMC 3 6.893 2.61e-05 1.990
Metro_vs_SMC 4 12.033 1.13e-07 3.474
DEMetro_Z_vs_SMC 0 7.015 2.23e-05 2.025
DEMetro_Z_vs_SMC 1 6.577 3.98e-05 1.899
DEMetro_Z_vs_SMC 2 7.519 1.17e-05 2.170
DEMetro_Z_vs_SMC 3 9.274 1.56e-06 2.677
DEMetro_Z_vs_SMC 4 11.246 2.26e-07 3.246
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 25.458 0.155 0.137 184.234
HMC 5 16.053 0.076 0.049 322.788
HMC 10 11.338 0.072 0.048 236.513
HMC 15 9.313 0.049 0.018 502.037
HMC 30 6.564 0.045 0.016 407.950
SMC 2 0.122 0.155 0.137 -0.244
SMC 5 0.113 0.076 0.049 0.742
SMC 10 0.093 0.072 0.048 0.447
SMC 15 0.064 0.049 0.018 0.765
SMC 30 0.053 0.045 0.016 0.468
Metro 2 23.361 0.155 0.137 168.967
Metro 5 16.058 0.076 0.049 322.892
Metro 10 10.419 0.072 0.048 217.214
Metro 15 7.260 0.049 0.018 390.802
Metro 30 6.067 0.045 0.016 376.857
DEMetro_Z 2 20.258 0.155 0.137 146.368
DEMetro_Z 5 18.648 0.076 0.049 375.216
DEMetro_Z 10 31.189 0.072 0.048 653.238
DEMetro_Z 15 22.613 0.049 0.018 1222.827
DEMetro_Z 30 19.140 0.045 0.016 1195.056
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 50.013 5.7e-15 84.579
HMC 5 36.874 5.46e-13 139.193
HMC 10 42.934 8.6e-14 127.820
HMC 15 58.729 1.3e-15 113.994
HMC 30 57.603 2.22e-15 129.889
SMC 2 -1.248 0.226 -0.481
SMC 5 1.188 0.247 0.479
SMC 10 0.153 0.88 0.072
SMC 15 0.100 0.922 0.050
SMC 30 -1.092 0.288 -0.381
Metro 2 11.266 2.14e-07 75.901
Metro 5 32.421 2.35e-12 133.949
Metro 10 21.416 2.36e-10 121.809
Metro 15 8.027 6.27e-06 88.947
Metro 30 14.991 1.11e-08 121.766
DEMetro_Z 2 7.854 7.67e-06 68.105
DEMetro_Z 5 10.536 4.35e-07 153.753
DEMetro_Z 10 10.801 3.4e-07 694.859
DEMetro_Z 15 13.428 3.63e-08 738.282
DEMetro_Z 30 17.877 1.77e-09 1367.156
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 0.664 0.52 0.192
Metro_vs_DEMetro_Z 1 -1.362 0.201 -0.393
Metro_vs_DEMetro_Z 2 -9.067 1.95e-06 -2.618
Metro_vs_DEMetro_Z 3 -10.886 3.14e-07 -3.143
Metro_vs_DEMetro_Z 4 -15.900 6.16e-09 -4.590
DEMetro_Z_vs_SMC 0 7.925 7.14e-06 2.288
DEMetro_Z_vs_SMC 1 10.576 4.21e-07 3.053
DEMetro_Z_vs_SMC 2 10.793 3.43e-07 3.116
DEMetro_Z_vs_SMC 3 13.438 3.61e-08 3.879
DEMetro_Z_vs_SMC 4 17.883 1.77e-09 5.163
HMC_vs_DEMetro_Z 0 1.840 0.0929 0.531
HMC_vs_DEMetro_Z 1 -0.904 0.385 -0.261
HMC_vs_DEMetro_Z 2 -8.679 2.99e-06 -2.505
HMC_vs_DEMetro_Z 3 -11.217 2.32e-07 -3.238
HMC_vs_DEMetro_Z 4 -16.285 4.78e-09 -4.701
HMC_vs_Metro 0 1.294 0.222 0.373
HMC_vs_Metro 1 0.794 0.444 0.229
HMC_vs_Metro 2 0.910 0.383 0.263
HMC_vs_Metro 3 2.462 0.0316 0.711
HMC_vs_Metro 4 0.952 0.361 0.275
HMC_vs_SMC 0 48.787 3.29e-14 14.084
HMC_vs_SMC 1 36.589 7.66e-13 10.562
HMC_vs_SMC 2 41.453 1.96e-13 11.967
HMC_vs_SMC 3 56.657 6.39e-15 16.356
HMC_vs_SMC 4 60.742 2.98e-15 17.535
Metro_vs_SMC 0 11.195 2.37e-07 3.232
Metro_vs_SMC 1 32.952 2.4e-12 9.512
Metro_vs_SMC 2 21.543 2.4e-10 6.219
Metro_vs_SMC 3 8.108 5.75e-06 2.341
Metro_vs_SMC 4 14.872 1.25e-08 4.293
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 3.861 0.103 0.044 84.579
HMC 5 2.369 0.051 0.017 139.193
HMC 10 1.541 0.047 0.012 127.820
HMC 15 1.236 0.042 0.010 113.994
HMC 30 0.894 0.040 0.007 129.889
SMC 2 0.081 0.103 0.044 -0.481
SMC 5 0.059 0.051 0.017 0.479
SMC 10 0.048 0.047 0.012 0.072
SMC 15 0.043 0.042 0.010 0.050
SMC 30 0.037 0.040 0.007 -0.381
Metro 2 3.476 0.103 0.044 75.901
Metro 5 2.281 0.051 0.017 133.949
Metro 10 1.470 0.047 0.012 121.809
Metro 15 0.974 0.042 0.010 88.947
Metro 30 0.840 0.040 0.007 121.766
DEMetro_Z 2 3.129 0.103 0.044 68.105
DEMetro_Z 5 2.611 0.051 0.017 153.753
DEMetro_Z 10 8.165 0.047 0.012 694.859
DEMetro_Z 15 7.773 0.042 0.010 738.282
DEMetro_Z 30 9.028 0.040 0.007 1367.156
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 123.404 1.41e-24 85.157
HMC 5 110.285 9.46e-20 136.501
HMC 10 96.468 5.04e-19 119.952
HMC 15 125.378 1.53e-21 122.506
HMC 30 102.305 4.02e-20 105.081
SMC 2 -1.246 0.226 -0.481
SMC 5 1.650 0.113 0.672
SMC 10 0.175 0.863 0.075
SMC 15 0.172 0.865 0.094
SMC 30 -1.051 0.307 -0.355
Metro 2 11.405 1.89e-07 77.725
Metro 5 125.602 6.35e-21 138.199
Metro 10 25.519 3.34e-11 114.789
Metro 15 7.901 7.3e-06 98.956
Metro 30 15.066 1.04e-08 98.345
DEMetro_Z 2 8.072 5.91e-06 70.507
DEMetro_Z 5 16.298 4.56e-09 121.478
DEMetro_Z 10 29.701 6.86e-12 187.564
DEMetro_Z 15 39.041 3.28e-13 201.073
DEMetro_Z 30 33.209 2.03e-12 214.560
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 8.146 5.5e-06 2.351
DEMetro_Z_vs_SMC 1 16.097 5.41e-09 4.647
DEMetro_Z_vs_SMC 2 30.014 6.63e-12 8.664
DEMetro_Z_vs_SMC 3 39.106 3.7e-13 11.289
DEMetro_Z_vs_SMC 4 33.731 1.86e-12 9.737
HMC_vs_Metro 0 1.127 0.284 0.325
HMC_vs_Metro 1 -1.138 0.279 -0.329
HMC_vs_Metro 2 1.060 0.312 0.306
HMC_vs_Metro 3 1.857 0.0903 0.536
HMC_vs_Metro 4 0.960 0.358 0.277
Metro_vs_DEMetro_Z 0 0.609 0.555 0.176
Metro_vs_DEMetro_Z 1 2.196 0.0505 0.634
Metro_vs_DEMetro_Z 2 -8.796 2.62e-06 -2.539
Metro_vs_DEMetro_Z 3 -7.529 1.16e-05 -2.173
Metro_vs_DEMetro_Z 4 -12.368 8.52e-08 -3.570
HMC_vs_SMC 0 145.990 1.95e-19 42.144
HMC_vs_SMC 1 111.067 3.94e-18 32.062
HMC_vs_SMC 2 91.514 3.31e-17 26.418
HMC_vs_SMC 3 127.462 8.68e-19 36.795
HMC_vs_SMC 4 108.068 5.33e-18 31.196
Metro_vs_SMC 0 11.416 1.94e-07 3.296
Metro_vs_SMC 1 110.567 4.14e-18 31.918
Metro_vs_SMC 2 25.984 3.17e-11 7.501
Metro_vs_SMC 3 7.941 7.01e-06 2.292
Metro_vs_SMC 4 14.925 1.2e-08 4.308
HMC_vs_DEMetro_Z 0 1.642 0.129 0.474
HMC_vs_DEMetro_Z 1 2.025 0.0679 0.584
HMC_vs_DEMetro_Z 2 -10.455 4.73e-07 -3.018
HMC_vs_DEMetro_Z 3 -15.365 8.84e-09 -4.436
HMC_vs_DEMetro_Z 4 -16.892 3.24e-09 -4.876
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.619 0.014 0.007 85.157
HMC 5 0.593 0.010 0.004 136.501
HMC 10 0.565 0.012 0.005 119.952
HMC 15 0.537 0.012 0.004 122.506
HMC 30 0.463 0.015 0.004 105.081
SMC 2 0.010 0.014 0.007 -0.481
SMC 5 0.012 0.010 0.004 0.672
SMC 10 0.013 0.012 0.005 0.075
SMC 15 0.013 0.012 0.004 0.094
SMC 30 0.013 0.015 0.004 -0.355
Metro 2 0.566 0.014 0.007 77.725
Metro 5 0.601 0.010 0.004 138.199
Metro 10 0.541 0.012 0.005 114.789
Metro 15 0.436 0.012 0.004 98.956
Metro 30 0.434 0.015 0.004 98.345
DEMetro_Z 2 0.515 0.014 0.007 70.507
DEMetro_Z 5 0.529 0.010 0.004 121.478
DEMetro_Z 10 0.876 0.012 0.005 187.564
DEMetro_Z 15 0.874 0.012 0.004 201.073
DEMetro_Z 30 0.929 0.015 0.004 214.560
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
2 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
30 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
30 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2
5
10
15
30
Chain
2
5
10
15
30

two_attr_mm

▼

Varying_Mode_Distance_with_high_Dimension (Mixture, mm, 12 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 3.335 0.0062 5.820
HMC 8 7.039 2.13e-05 53.533
HMC 10 5.548 0.000172 49.141
HMC 12 4.050 0.00191 54.186
HMC 15 3.306 0.00697 26.361
HMC 18 2.413 0.0344 18.050
SMC 5 0.826 0.419 0.445
SMC 8 0.924 0.366 0.442
SMC 10 0.825 0.419 0.294
SMC 12 2.552 0.0188 1.218
SMC 15 0.671 0.509 0.255
SMC 18 -0.618 0.543 -0.258
Metro 5 6.937 1.53e-05 9.379
Metro 8 5.178 0.000298 26.605
Metro 10 5.417 0.000206 27.500
Metro 12 4.468 0.000945 44.479
Metro 15 3.385 0.00607 26.610
Metro 18 2.959 0.013 21.599
DEMetro_Z 5 22.177 1.76e-10 2813.387
DEMetro_Z 8 32.172 3.11e-12 1552.602
DEMetro_Z 10 23.973 7.57e-11 740.903
DEMetro_Z 12 36.434 7.98e-13 889.749
DEMetro_Z 15 45.452 6.66e-14 340.806
DEMetro_Z 18 23.865 7.86e-11 337.535
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -22.038 1.88e-10 -6.362
HMC_vs_DEMetro_Z 1 -32.515 2.78e-12 -9.386
HMC_vs_DEMetro_Z 2 -25.181 4.46e-11 -7.269
HMC_vs_DEMetro_Z 3 -31.794 3.54e-12 -9.178
HMC_vs_DEMetro_Z 4 -26.658 2.41e-11 -7.695
HMC_vs_DEMetro_Z 5 -19.215 8.21e-10 -5.547
Metro_vs_SMC 0 6.406 5.04e-05 1.849
Metro_vs_SMC 1 5.009 0.000397 1.446
Metro_vs_SMC 2 5.330 0.000241 1.539
Metro_vs_SMC 3 4.322 0.00121 1.248
Metro_vs_SMC 4 3.361 0.00636 0.970
Metro_vs_SMC 5 3.011 0.0118 0.869
Metro_vs_DEMetro_Z 0 -21.974 1.94e-10 -6.343
Metro_vs_DEMetro_Z 1 -32.146 3.14e-12 -9.280
Metro_vs_DEMetro_Z 2 -24.477 6.06e-11 -7.066
Metro_vs_DEMetro_Z 3 -34.570 1.42e-12 -9.979
Metro_vs_DEMetro_Z 4 -26.890 2.19e-11 -7.763
Metro_vs_DEMetro_Z 5 -19.834 5.84e-10 -5.726
HMC_vs_Metro 0 -1.720 0.113 -0.496
HMC_vs_Metro 1 3.628 0.00397 1.047
HMC_vs_Metro 2 2.135 0.0561 0.616
HMC_vs_Metro 3 1.111 0.29 0.321
HMC_vs_Metro 4 -1.508 0.16 -0.435
HMC_vs_Metro 5 -1.150 0.275 -0.332
HMC_vs_SMC 0 3.553 0.00453 1.026
HMC_vs_SMC 1 7.077 2.05e-05 2.043
HMC_vs_SMC 2 5.522 0.00018 1.594
HMC_vs_SMC 3 3.931 0.00235 1.135
HMC_vs_SMC 4 3.282 0.0073 0.948
HMC_vs_SMC 5 2.465 0.0314 0.711
DEMetro_Z_vs_SMC 0 22.139 1.79e-10 6.391
DEMetro_Z_vs_SMC 1 32.037 3.26e-12 9.248
DEMetro_Z_vs_SMC 2 23.958 7.64e-11 6.916
DEMetro_Z_vs_SMC 3 36.415 8.07e-13 10.512
DEMetro_Z_vs_SMC 4 44.592 8.81e-14 12.873
DEMetro_Z_vs_SMC 5 23.905 7.83e-11 6.901
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.036 0.023 0.002 5.820
HMC 8 0.261 0.025 0.004 53.533
HMC 10 0.454 0.026 0.009 49.141
HMC 12 0.414 0.030 0.007 54.186
HMC 15 0.529 0.035 0.019 26.361
HMC 18 0.420 0.044 0.021 18.050
SMC 5 0.024 0.023 0.002 0.445
SMC 8 0.027 0.025 0.004 0.442
SMC 10 0.029 0.026 0.009 0.294
SMC 12 0.038 0.030 0.007 1.218
SMC 15 0.040 0.035 0.019 0.255
SMC 18 0.039 0.044 0.021 -0.258
Metro 5 0.043 0.023 0.002 9.379
Metro 8 0.142 0.025 0.004 26.605
Metro 10 0.266 0.026 0.009 27.500
Metro 12 0.345 0.030 0.007 44.479
Metro 15 0.534 0.035 0.019 26.610
Metro 18 0.494 0.044 0.021 21.599
DEMetro_Z 5 6.211 0.023 0.002 2813.387
DEMetro_Z 8 6.864 0.025 0.004 1552.602
DEMetro_Z 10 6.475 0.026 0.009 740.903
DEMetro_Z 12 6.338 0.030 0.007 889.749
DEMetro_Z 15 6.427 0.035 0.019 340.806
DEMetro_Z 18 7.076 0.044 0.021 337.535
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 1.619 0.121 0.569
HMC 8 3.229 0.00798 20.123
HMC 10 3.487 0.00508 141.997
HMC 12 2.898 0.0145 101.070
HMC 15 2.609 0.0243 145.557
HMC 18 2.009 0.0698 113.693
SMC 5 1.560 0.133 0.594
SMC 8 1.231 0.233 0.441
SMC 10 2.570 0.0186 1.331
SMC 12 3.103 0.00607 1.713
SMC 15 2.656 0.018 1.930
SMC 18 2.142 0.0467 1.266
Metro 5 4.691 0.000112 1.908
Metro 8 2.611 0.0236 5.467
Metro 10 3.608 0.00411 48.276
Metro 12 4.148 0.00162 66.358
Metro 15 2.646 0.0228 146.873
Metro 18 2.290 0.0428 127.253
DEMetro_Z 5 15.719 6.95e-09 15593.646
DEMetro_Z 8 21.441 2.53e-10 8248.656
DEMetro_Z 10 27.056 2.05e-11 17586.087
DEMetro_Z 12 20.717 3.66e-10 12096.115
DEMetro_Z 15 26.889 2.19e-11 9396.415
DEMetro_Z 18 24.992 4.84e-11 7794.524
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -0.075 0.942 -0.022
HMC_vs_SMC 1 3.159 0.0091 0.912
HMC_vs_SMC 2 3.457 0.00536 0.998
HMC_vs_SMC 3 2.862 0.0155 0.826
HMC_vs_SMC 4 2.575 0.0258 0.743
HMC_vs_SMC 5 1.988 0.0722 0.574
Metro_vs_DEMetro_Z 0 -15.717 6.97e-09 -4.537
Metro_vs_DEMetro_Z 1 -21.453 2.52e-10 -6.193
Metro_vs_DEMetro_Z 2 -26.903 2.18e-11 -7.766
Metro_vs_DEMetro_Z 3 -20.274 4.62e-10 -5.853
Metro_vs_DEMetro_Z 4 -24.977 4.87e-11 -7.210
Metro_vs_DEMetro_Z 5 -25.421 4.03e-11 -7.338
HMC_vs_Metro 0 -4.856 0.000506 -1.402
HMC_vs_Metro 1 2.451 0.0322 0.707
HMC_vs_Metro 2 2.165 0.0533 0.625
HMC_vs_Metro 3 1.216 0.249 0.351
HMC_vs_Metro 4 -1.845 0.0921 -0.533
HMC_vs_Metro 5 -0.960 0.358 -0.277
HMC_vs_DEMetro_Z 0 -15.717 6.97e-09 -4.537
HMC_vs_DEMetro_Z 1 -21.415 2.56e-10 -6.182
HMC_vs_DEMetro_Z 2 -26.254 2.84e-11 -7.579
HMC_vs_DEMetro_Z 3 -20.229 4.73e-10 -5.840
HMC_vs_DEMetro_Z 4 -24.984 4.86e-11 -7.212
HMC_vs_DEMetro_Z 5 -25.305 4.23e-11 -7.305
Metro_vs_SMC 0 3.922 0.00238 1.132
Metro_vs_SMC 1 2.513 0.0289 0.725
Metro_vs_SMC 2 3.545 0.00459 1.023
Metro_vs_SMC 3 4.053 0.00191 1.170
Metro_vs_SMC 4 2.612 0.0242 0.754
Metro_vs_SMC 5 2.270 0.0443 0.655
DEMetro_Z_vs_SMC 0 15.719 6.96e-09 4.538
DEMetro_Z_vs_SMC 1 21.443 2.53e-10 6.190
DEMetro_Z_vs_SMC 2 27.050 2.05e-11 7.809
DEMetro_Z_vs_SMC 3 20.715 3.67e-10 5.980
DEMetro_Z_vs_SMC 4 26.895 2.18e-11 7.764
DEMetro_Z_vs_SMC 5 24.991 4.84e-11 7.214
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.047 0.041 0.011 0.569
HMC 8 0.446 0.046 0.020 20.123
HMC 10 1.511 0.040 0.010 141.997
HMC 12 1.529 0.045 0.015 101.070
HMC 15 2.827 0.044 0.019 145.557
HMC 18 2.516 0.053 0.022 113.693
SMC 5 0.047 0.041 0.011 0.594
SMC 8 0.055 0.046 0.020 0.441
SMC 10 0.053 0.040 0.010 1.331
SMC 12 0.070 0.045 0.015 1.713
SMC 15 0.081 0.044 0.019 1.930
SMC 18 0.080 0.053 0.022 1.266
Metro 5 0.062 0.041 0.011 1.908
Metro 8 0.155 0.046 0.020 5.467
Metro 10 0.540 0.040 0.010 48.276
Metro 12 1.019 0.045 0.015 66.358
Metro 15 2.852 0.044 0.019 146.873
Metro 18 2.810 0.053 0.022 127.253
DEMetro_Z 5 172.242 0.041 0.011 15593.646
DEMetro_Z 8 163.985 0.046 0.020 8248.656
DEMetro_Z 10 182.308 0.040 0.010 17586.087
DEMetro_Z 12 177.630 0.045 0.015 12096.115
DEMetro_Z 15 179.662 0.044 0.019 9396.415
DEMetro_Z 18 168.934 0.053 0.022 7794.524
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 3.656 0.00353 7.212
HMC 8 6.720 3.26e-05 66.937
HMC 10 5.376 0.000224 58.728
HMC 12 4.169 0.00156 78.893
HMC 15 3.315 0.00688 31.712
HMC 18 2.418 0.0341 21.035
SMC 5 2.236 0.0371 1.133
SMC 8 1.240 0.229 0.560
SMC 10 1.159 0.261 0.405
SMC 12 3.412 0.00301 1.854
SMC 15 1.042 0.309 0.396
SMC 18 -0.625 0.538 -0.253
Metro 5 7.813 4.88e-06 10.997
Metro 8 5.301 0.000249 34.072
Metro 10 5.148 0.000315 31.407
Metro 12 4.477 0.000934 67.048
Metro 15 3.429 0.00562 33.663
Metro 18 3.005 0.0119 25.242
DEMetro_Z 5 37.043 6.69e-13 7269.545
DEMetro_Z 8 48.009 3.92e-14 3833.302
DEMetro_Z 10 56.170 7e-15 1765.269
DEMetro_Z 12 46.165 6.02e-14 2617.362
DEMetro_Z 15 54.333 9.93e-15 829.364
DEMetro_Z 18 38.576 4.25e-13 699.696
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -37.004 6.77e-13 -10.682
Metro_vs_DEMetro_Z 1 -47.705 4.21e-14 -13.771
Metro_vs_DEMetro_Z 2 -53.648 1.16e-14 -15.487
Metro_vs_DEMetro_Z 3 -39.194 3.61e-13 -11.314
Metro_vs_DEMetro_Z 4 -40.673 2.41e-13 -11.741
Metro_vs_DEMetro_Z 5 -34.039 1.68e-12 -9.826
DEMetro_Z_vs_SMC 0 37.060 6.66e-13 10.698
DEMetro_Z_vs_SMC 1 48.027 3.91e-14 13.864
DEMetro_Z_vs_SMC 2 56.130 7.08e-15 16.203
DEMetro_Z_vs_SMC 3 46.044 6.2e-14 13.292
DEMetro_Z_vs_SMC 4 54.004 1.08e-14 15.590
DEMetro_Z_vs_SMC 5 38.519 4.37e-13 11.119
HMC_vs_DEMetro_Z 0 -37.069 6.64e-13 -10.701
HMC_vs_DEMetro_Z 1 -47.553 4.36e-14 -13.727
HMC_vs_DEMetro_Z 2 -55.682 7.73e-15 -16.074
HMC_vs_DEMetro_Z 3 -38.627 4.24e-13 -11.151
HMC_vs_DEMetro_Z 4 -41.076 2.16e-13 -11.858
HMC_vs_DEMetro_Z 5 -32.721 2.59e-12 -9.446
HMC_vs_Metro 0 -1.763 0.106 -0.509
HMC_vs_Metro 1 3.454 0.00539 0.997
HMC_vs_Metro 2 2.162 0.0535 0.624
HMC_vs_Metro 3 1.029 0.325 0.297
HMC_vs_Metro 4 -2.346 0.0388 -0.677
HMC_vs_Metro 5 -1.117 0.288 -0.323
HMC_vs_SMC 0 3.547 0.00457 1.024
HMC_vs_SMC 1 6.723 3.27e-05 1.941
HMC_vs_SMC 2 5.343 0.000236 1.542
HMC_vs_SMC 3 4.052 0.00191 1.170
HMC_vs_SMC 4 3.280 0.00734 0.947
HMC_vs_SMC 5 2.463 0.0315 0.711
Metro_vs_SMC 0 6.781 3.03e-05 1.957
Metro_vs_SMC 1 5.153 0.000317 1.488
Metro_vs_SMC 2 5.076 0.000357 1.465
Metro_vs_SMC 3 4.345 0.00117 1.254
Metro_vs_SMC 4 3.395 0.00598 0.980
Metro_vs_SMC 5 3.050 0.011 0.880
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.040 0.030 0.001 7.212
HMC 8 0.208 0.033 0.003 66.937
HMC 10 0.372 0.035 0.006 58.728
HMC 12 0.333 0.037 0.004 78.893
HMC 15 0.422 0.041 0.012 31.712
HMC 18 0.343 0.049 0.014 21.035
SMC 5 0.032 0.030 0.001 1.133
SMC 8 0.034 0.033 0.003 0.560
SMC 10 0.037 0.035 0.006 0.405
SMC 12 0.044 0.037 0.004 1.854
SMC 15 0.046 0.041 0.012 0.396
SMC 18 0.046 0.049 0.014 -0.253
Metro 5 0.045 0.030 0.001 10.997
Metro 8 0.122 0.033 0.003 34.072
Metro 10 0.215 0.035 0.006 31.407
Metro 12 0.289 0.037 0.004 67.048
Metro 15 0.446 0.041 0.012 33.663
Metro 18 0.402 0.049 0.014 25.242
DEMetro_Z 5 10.041 0.030 0.001 7269.545
DEMetro_Z 8 10.062 0.033 0.003 3833.302
DEMetro_Z 10 10.187 0.035 0.006 1765.269
DEMetro_Z 12 9.882 0.037 0.004 2617.362
DEMetro_Z 15 10.005 0.041 0.012 829.364
DEMetro_Z 18 9.813 0.049 0.014 699.696
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 3.741 0.00285 5.390
HMC 8 6.986 2.28e-05 52.353
HMC 10 5.571 0.000166 52.333
HMC 12 3.959 0.00224 69.856
HMC 15 3.326 0.00675 33.022
HMC 18 2.450 0.0322 24.578
SMC 5 1.738 0.0969 0.800
SMC 8 1.329 0.197 0.563
SMC 10 0.846 0.408 0.290
SMC 12 3.256 0.00387 1.559
SMC 15 0.848 0.406 0.327
SMC 18 -0.239 0.814 -0.114
Metro 5 7.730 4.11e-06 8.769
Metro 8 5.101 0.000336 25.760
Metro 10 5.408 0.00021 28.586
Metro 12 4.453 0.000972 57.681
Metro 15 3.432 0.00559 32.344
Metro 18 2.960 0.013 31.160
DEMetro_Z 5 43.295 1.18e-13 458.419
DEMetro_Z 8 101.041 5.38e-18 276.960
DEMetro_Z 10 59.555 1.96e-15 158.534
DEMetro_Z 12 70.536 3.93e-16 248.677
DEMetro_Z 15 52.918 3.51e-15 94.827
DEMetro_Z 18 50.152 1.03e-14 110.695
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 42.916 1.34e-13 12.389
DEMetro_Z_vs_SMC 1 98.019 1.56e-17 28.296
DEMetro_Z_vs_SMC 2 60.025 3.39e-15 17.328
DEMetro_Z_vs_SMC 3 68.966 7.4e-16 19.909
DEMetro_Z_vs_SMC 4 53.901 1.1e-14 15.560
DEMetro_Z_vs_SMC 5 48.759 3.31e-14 14.075
HMC_vs_Metro 0 -1.949 0.0772 -0.563
HMC_vs_Metro 1 3.430 0.00562 0.990
HMC_vs_Metro 2 2.196 0.0504 0.634
HMC_vs_Metro 3 1.068 0.308 0.308
HMC_vs_Metro 4 0.990 0.343 0.286
HMC_vs_Metro 5 -1.536 0.153 -0.443
Metro_vs_DEMetro_Z 0 -40.392 2.6e-13 -11.660
Metro_vs_DEMetro_Z 1 -53.715 1.15e-14 -15.506
Metro_vs_DEMetro_Z 2 -25.729 3.53e-11 -7.427
Metro_vs_DEMetro_Z 3 -15.294 9.29e-09 -4.415
Metro_vs_DEMetro_Z 4 -6.292 5.9e-05 -1.816
Metro_vs_DEMetro_Z 5 -8.074 5.98e-06 -2.331
HMC_vs_SMC 0 3.802 0.00293 1.098
HMC_vs_SMC 1 7.034 2.17e-05 2.031
HMC_vs_SMC 2 5.549 0.000173 1.602
HMC_vs_SMC 3 3.845 0.00272 1.110
HMC_vs_SMC 4 3.305 0.00701 0.954
HMC_vs_SMC 5 2.461 0.0316 0.711
Metro_vs_SMC 0 6.950 2.42e-05 2.006
Metro_vs_SMC 1 4.950 0.000436 1.429
Metro_vs_SMC 2 5.339 0.000238 1.541
Metro_vs_SMC 3 4.295 0.00127 1.240
Metro_vs_SMC 4 3.411 0.00582 0.985
Metro_vs_SMC 5 2.963 0.0129 0.855
HMC_vs_DEMetro_Z 0 -41.858 1.76e-13 -12.083
HMC_vs_DEMetro_Z 1 -25.010 4.8e-11 -7.220
HMC_vs_DEMetro_Z 2 -12.037 1.13e-07 -3.475
HMC_vs_DEMetro_Z 3 -11.053 2.69e-07 -3.191
HMC_vs_DEMetro_Z 4 -5.942 9.7e-05 -1.715
HMC_vs_DEMetro_Z 5 -9.290 1.54e-06 -2.682
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.020 0.013 0.001 5.390
HMC 8 0.119 0.013 0.002 52.353
HMC 10 0.196 0.013 0.004 52.333
HMC 12 0.170 0.013 0.002 69.856
HMC 15 0.200 0.013 0.006 33.022
HMC 18 0.137 0.014 0.005 24.578
SMC 5 0.014 0.013 0.001 0.800
SMC 8 0.014 0.013 0.002 0.563
SMC 10 0.014 0.013 0.004 0.290
SMC 12 0.017 0.013 0.002 1.559
SMC 15 0.015 0.013 0.006 0.327
SMC 18 0.014 0.014 0.005 -0.114
Metro 5 0.024 0.013 0.001 8.769
Metro 8 0.065 0.013 0.002 25.760
Metro 10 0.113 0.013 0.004 28.586
Metro 12 0.142 0.013 0.002 57.681
Metro 15 0.197 0.013 0.006 32.344
Metro 18 0.169 0.014 0.005 31.160
DEMetro_Z 5 0.575 0.013 0.001 458.419
DEMetro_Z 8 0.573 0.013 0.002 276.960
DEMetro_Z 10 0.569 0.013 0.004 158.534
DEMetro_Z 12 0.570 0.013 0.002 248.677
DEMetro_Z 15 0.551 0.013 0.006 94.827
DEMetro_Z 18 0.565 0.014 0.005 110.695
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 3.018 0.0112 6.106
HMC 8 5.052 0.000371 96.304
HMC 10 156.994 4.58e-27 102.091
HMC 12 177.193 1.07e-24 149.019
HMC 15 159.395 1.82e-34 70.992
HMC 18 164.808 4.85e-34 76.613
SMC 5 1.645 0.117 0.903
SMC 8 1.082 0.291 0.434
SMC 10 0.972 0.342 0.437
SMC 12 1.402 0.179 0.876
SMC 15 0.060 0.953 0.021
SMC 18 -0.404 0.69 -0.157
Metro 5 6.594 2.66e-05 9.541
Metro 8 4.785 0.000559 28.853
Metro 10 3.346 0.00651 36.781
Metro 12 29.774 6.31e-12 144.587
Metro 15 153.298 1.88e-33 70.997
Metro 18 145.859 1.83e-30 76.612
DEMetro_Z 5 16.738 3.58e-09 4689.347
DEMetro_Z 8 14.456 1.68e-08 2458.663
DEMetro_Z 10 16.136 5.27e-09 1247.983
DEMetro_Z 12 11.509 1.78e-07 1391.846
DEMetro_Z 15 16.533 4.07e-09 544.160
DEMetro_Z 18 18.772 1.05e-09 482.105
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -16.760 3.53e-09 -4.838
HMC_vs_DEMetro_Z 1 -13.835 2.66e-08 -3.994
HMC_vs_DEMetro_Z 2 -14.784 1.33e-08 -4.268
HMC_vs_DEMetro_Z 3 -10.276 5.63e-07 -2.966
HMC_vs_DEMetro_Z 4 -14.373 1.79e-08 -4.149
HMC_vs_DEMetro_Z 5 -15.746 6.83e-09 -4.545
Metro_vs_SMC 0 5.083 0.000353 1.467
Metro_vs_SMC 1 4.635 0.000722 1.338
Metro_vs_SMC 2 3.318 0.00686 0.958
Metro_vs_SMC 3 28.371 1.22e-11 8.190
Metro_vs_SMC 4 165.271 4.99e-20 47.710
Metro_vs_SMC 5 170.335 3.58e-20 49.172
Metro_vs_DEMetro_Z 0 -16.721 3.61e-09 -4.827
Metro_vs_DEMetro_Z 1 -14.258 1.94e-08 -4.116
Metro_vs_DEMetro_Z 2 -16.049 5.58e-09 -4.633
Metro_vs_DEMetro_Z 3 -10.273 5.64e-07 -2.966
Metro_vs_DEMetro_Z 4 -14.380 1.78e-08 -4.151
Metro_vs_DEMetro_Z 5 -15.733 6.89e-09 -4.542
HMC_vs_Metro 0 -1.394 0.191 -0.402
HMC_vs_Metro 1 3.421 0.00572 0.987
HMC_vs_Metro 2 5.847 0.000111 1.688
HMC_vs_Metro 3 0.973 0.352 0.281
HMC_vs_Metro 4 -0.057 0.955 -0.016
HMC_vs_Metro 5 0.005 0.996 0.002
HMC_vs_SMC 0 2.792 0.0175 0.806
HMC_vs_SMC 1 5.020 0.00039 1.449
HMC_vs_SMC 2 126.356 9.55e-19 36.476
HMC_vs_SMC 3 134.410 4.84e-19 38.801
HMC_vs_SMC 4 167.151 4.41e-20 48.252
HMC_vs_SMC 5 217.073 2.49e-21 62.663
DEMetro_Z_vs_SMC 0 16.742 3.57e-09 4.833
DEMetro_Z_vs_SMC 1 14.468 1.67e-08 4.177
DEMetro_Z_vs_SMC 2 16.149 5.23e-09 4.662
DEMetro_Z_vs_SMC 3 11.494 1.81e-07 3.318
DEMetro_Z_vs_SMC 4 16.518 4.12e-09 4.768
DEMetro_Z_vs_SMC 5 18.834 1.02e-09 5.437
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.036 0.023 0.002 6.106
HMC 8 0.449 0.025 0.004 96.304
HMC 10 0.915 0.026 0.009 102.091
HMC 12 1.086 0.030 0.007 149.019
HMC 15 1.367 0.035 0.019 70.992
HMC 18 1.640 0.044 0.021 76.613
SMC 5 0.025 0.023 0.002 0.903
SMC 8 0.027 0.025 0.004 0.434
SMC 10 0.030 0.026 0.009 0.437
SMC 12 0.036 0.030 0.007 0.876
SMC 15 0.035 0.035 0.019 0.021
SMC 18 0.041 0.044 0.021 -0.157
Metro 5 0.044 0.023 0.002 9.541
Metro 8 0.152 0.025 0.004 28.853
Metro 10 0.347 0.026 0.009 36.781
Metro 12 1.055 0.030 0.007 144.587
Metro 15 1.367 0.035 0.019 70.997
Metro 18 1.640 0.044 0.021 76.612
DEMetro_Z 5 10.338 0.023 0.002 4689.347
DEMetro_Z 8 10.856 0.025 0.004 2458.663
DEMetro_Z 10 10.889 0.026 0.009 1247.983
DEMetro_Z 12 9.898 0.030 0.007 1391.846
DEMetro_Z 15 10.242 0.035 0.019 544.160
DEMetro_Z 18 10.087 0.044 0.021 482.105
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 1.306 0.205 0.577
HMC 8 3.876 0.00258 73.272
HMC 10 496.000 2.02e-30 434.778
HMC 12 758.922 9.27e-41 444.734
HMC 15 821.429 1.47e-38 535.737
HMC 18 889.173 7.07e-36 680.021
SMC 5 -1.360 0.194 -0.425
SMC 8 -0.950 0.354 -0.323
SMC 10 1.336 0.2 0.851
SMC 12 1.640 0.121 1.075
SMC 15 2.702 0.0138 1.351
SMC 18 1.936 0.0679 1.023
Metro 5 3.685 0.00146 1.807
Metro 8 2.551 0.0266 7.249
Metro 10 2.542 0.0274 118.851
Metro 12 17.470 2.26e-09 420.862
Metro 15 860.668 4.9e-40 535.971
Metro 18 934.426 4.37e-37 680.212
DEMetro_Z 5 7.531 1.16e-05 1994.308
DEMetro_Z 8 8.553 3.44e-06 1016.153
DEMetro_Z 10 12.738 6.28e-08 1883.917
DEMetro_Z 12 17.992 1.66e-09 1437.774
DEMetro_Z 15 12.513 7.56e-08 1136.426
DEMetro_Z 18 12.827 5.84e-08 1173.729
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 3.054 0.011 0.882
HMC_vs_SMC 1 3.899 0.00248 1.126
HMC_vs_SMC 2 335.614 2.06e-23 96.883
HMC_vs_SMC 3 1257.572 1.01e-29 363.030
HMC_vs_SMC 4 1129.955 3.28e-29 326.190
HMC_vs_SMC 5 853.099 7.21e-28 246.269
Metro_vs_DEMetro_Z 0 -7.521 1.17e-05 -2.171
Metro_vs_DEMetro_Z 1 -8.462 3.81e-06 -2.443
Metro_vs_DEMetro_Z 2 -14.010 2.33e-08 -4.044
Metro_vs_DEMetro_Z 3 -12.626 6.89e-08 -3.645
Metro_vs_DEMetro_Z 4 -6.628 3.72e-05 -1.913
Metro_vs_DEMetro_Z 5 -5.377 0.000224 -1.552
HMC_vs_Metro 0 -3.781 0.00304 -1.091
HMC_vs_Metro 1 3.523 0.00477 1.017
HMC_vs_Metro 2 6.791 2.99e-05 1.960
HMC_vs_Metro 3 0.990 0.344 0.286
HMC_vs_Metro 4 -1.582 0.142 -0.457
HMC_vs_Metro 5 -1.912 0.0822 -0.552
HMC_vs_DEMetro_Z 0 -7.527 1.16e-05 -2.173
HMC_vs_DEMetro_Z 1 -7.699 9.39e-06 -2.222
HMC_vs_DEMetro_Z 2 -9.822 8.84e-07 -2.835
HMC_vs_DEMetro_Z 3 -12.378 8.45e-08 -3.573
HMC_vs_DEMetro_Z 4 -6.630 3.71e-05 -1.914
HMC_vs_DEMetro_Z 5 -5.375 0.000225 -1.552
Metro_vs_SMC 0 6.128 7.44e-05 1.769
Metro_vs_SMC 1 2.616 0.024 0.755
Metro_vs_SMC 2 2.522 0.0284 0.728
Metro_vs_SMC 3 17.321 2.49e-09 5.000
Metro_vs_SMC 4 1193.027 1.8e-29 344.397
Metro_vs_SMC 5 891.520 4.44e-28 257.360
DEMetro_Z_vs_SMC 0 7.533 1.15e-05 2.175
DEMetro_Z_vs_SMC 1 8.562 3.41e-06 2.472
DEMetro_Z_vs_SMC 2 12.730 6.33e-08 3.675
DEMetro_Z_vs_SMC 3 17.931 1.72e-09 5.176
DEMetro_Z_vs_SMC 4 12.523 7.49e-08 3.615
DEMetro_Z_vs_SMC 5 12.829 5.84e-08 3.704
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.047 0.041 0.011 0.577
HMC 8 1.503 0.046 0.020 73.272
HMC 10 4.546 0.040 0.010 434.778
HMC 12 6.574 0.045 0.015 444.734
HMC 15 10.285 0.044 0.019 535.737
HMC 18 14.787 0.053 0.022 680.021
SMC 5 0.036 0.041 0.011 -0.425
SMC 8 0.040 0.046 0.020 -0.323
SMC 10 0.048 0.040 0.010 0.851
SMC 12 0.061 0.045 0.015 1.075
SMC 15 0.070 0.044 0.019 1.351
SMC 18 0.075 0.053 0.022 1.023
Metro 5 0.061 0.041 0.011 1.807
Metro 8 0.190 0.046 0.020 7.249
Metro 10 1.271 0.040 0.010 118.851
Metro 12 6.224 0.045 0.015 420.862
Metro 15 10.290 0.044 0.019 535.971
Metro 18 14.791 0.053 0.022 680.212
DEMetro_Z 5 22.064 0.041 0.011 1994.308
DEMetro_Z 8 20.242 0.046 0.020 1016.153
DEMetro_Z 10 19.565 0.040 0.010 1883.917
DEMetro_Z 12 21.153 0.045 0.015 1437.774
DEMetro_Z 15 21.768 0.044 0.019 1136.426
DEMetro_Z 18 25.484 0.053 0.022 1173.729
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 3.307 0.0067 7.519
HMC 8 5.028 0.000385 126.336
HMC 10 115.711 7.45e-21 117.858
HMC 12 74.567 1.78e-16 219.087
HMC 15 74.426 9.23e-18 89.151
HMC 18 79.088 2.73e-18 89.386
SMC 5 1.917 0.072 1.137
SMC 8 0.798 0.434 0.336
SMC 10 0.956 0.35 0.420
SMC 12 1.844 0.0847 1.310
SMC 15 0.382 0.707 0.132
SMC 18 -0.379 0.708 -0.153
Metro 5 7.275 1.09e-05 11.301
Metro 8 4.768 0.000578 37.211
Metro 10 3.245 0.00779 43.274
Metro 12 27.694 1.51e-11 214.335
Metro 15 57.996 6.89e-16 87.983
Metro 18 67.931 6.12e-17 91.940
DEMetro_Z 5 17.152 2.76e-09 6258.291
DEMetro_Z 8 15.277 9.4e-09 3464.455
DEMetro_Z 10 17.555 2.15e-09 1574.680
DEMetro_Z 12 12.336 8.75e-08 2162.534
DEMetro_Z 15 16.529 4.08e-09 702.536
DEMetro_Z 18 19.492 7.02e-10 612.086
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -17.141 2.78e-09 -4.948
Metro_vs_DEMetro_Z 1 -15.107 1.06e-08 -4.361
Metro_vs_DEMetro_Z 2 -17.465 2.28e-09 -5.042
Metro_vs_DEMetro_Z 3 -11.215 2.32e-07 -3.238
Metro_vs_DEMetro_Z 4 -14.455 1.68e-08 -4.173
Metro_vs_DEMetro_Z 5 -16.488 4.19e-09 -4.760
DEMetro_Z_vs_SMC 0 17.149 2.76e-09 4.950
DEMetro_Z_vs_SMC 1 15.287 9.33e-09 4.413
DEMetro_Z_vs_SMC 2 17.567 2.14e-09 5.071
DEMetro_Z_vs_SMC 3 12.323 8.85e-08 3.557
DEMetro_Z_vs_SMC 4 16.520 4.11e-09 4.769
DEMetro_Z_vs_SMC 5 19.528 6.9e-10 5.637
HMC_vs_DEMetro_Z 0 -17.161 2.74e-09 -4.954
HMC_vs_DEMetro_Z 1 -14.561 1.56e-08 -4.203
HMC_vs_DEMetro_Z 2 -16.282 4.79e-09 -4.700
HMC_vs_DEMetro_Z 3 -11.074 2.64e-07 -3.197
HMC_vs_DEMetro_Z 4 -14.640 1.47e-08 -4.226
HMC_vs_DEMetro_Z 5 -16.850 3.33e-09 -4.864
HMC_vs_Metro 0 -1.424 0.182 -0.411
HMC_vs_Metro 1 3.365 0.0063 0.971
HMC_vs_Metro 2 5.781 0.000123 1.669
HMC_vs_Metro 3 0.623 0.546 0.180
HMC_vs_Metro 4 0.751 0.469 0.217
HMC_vs_Metro 5 -1.360 0.201 -0.393
HMC_vs_SMC 0 3.122 0.00972 0.901
HMC_vs_SMC 1 5.009 0.000397 1.446
HMC_vs_SMC 2 128.727 7.78e-19 37.160
HMC_vs_SMC 3 69.183 7.14e-16 19.971
HMC_vs_SMC 4 73.190 3.85e-16 21.128
HMC_vs_SMC 5 83.600 8.94e-17 24.133
Metro_vs_SMC 0 5.675 0.000143 1.638
Metro_vs_SMC 1 4.672 0.000681 1.349
Metro_vs_SMC 2 3.219 0.00817 0.929
Metro_vs_SMC 3 26.409 2.66e-11 7.624
Metro_vs_SMC 4 57.478 5.46e-15 16.592
Metro_vs_SMC 5 70.346 5.95e-16 20.307
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.040 0.030 0.001 7.519
HMC 8 0.363 0.033 0.003 126.336
HMC 10 0.712 0.035 0.006 117.858
HMC 12 0.861 0.037 0.004 219.087
HMC 15 1.112 0.041 0.012 89.151
HMC 18 1.297 0.049 0.014 89.386
SMC 5 0.032 0.030 0.001 1.137
SMC 8 0.034 0.033 0.003 0.336
SMC 10 0.037 0.035 0.006 0.420
SMC 12 0.042 0.037 0.004 1.310
SMC 15 0.043 0.041 0.012 0.132
SMC 18 0.047 0.049 0.014 -0.153
Metro 5 0.046 0.030 0.001 11.301
Metro 8 0.130 0.033 0.003 37.211
Metro 10 0.284 0.035 0.006 43.274
Metro 12 0.843 0.037 0.004 214.335
Metro 15 1.098 0.041 0.012 87.983
Metro 18 1.332 0.049 0.014 91.940
DEMetro_Z 5 8.649 0.030 0.001 6258.291
DEMetro_Z 8 9.097 0.033 0.003 3464.455
DEMetro_Z 10 9.091 0.035 0.006 1574.680
DEMetro_Z 12 8.172 0.037 0.004 2162.534
DEMetro_Z 15 8.482 0.041 0.012 702.536
DEMetro_Z 18 8.591 0.049 0.014 612.086
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 3.160 0.0085 5.374
HMC 8 4.988 0.00041 94.721
HMC 10 77.536 1.76e-17 111.862
HMC 12 103.290 1.86e-18 195.891
HMC 15 80.016 1.78e-18 87.575
HMC 18 103.445 3.08e-20 105.146
SMC 5 1.838 0.0797 0.790
SMC 8 1.240 0.229 0.457
SMC 10 0.818 0.422 0.360
SMC 12 1.567 0.137 1.053
SMC 15 0.249 0.806 0.083
SMC 18 -0.094 0.926 -0.045
Metro 5 6.803 1.78e-05 8.798
Metro 8 4.959 0.000423 27.114
Metro 10 3.310 0.00695 39.689
Metro 12 26.983 1.98e-11 186.618
Metro 15 128.146 5.04e-25 87.127
Metro 18 105.386 1.83e-20 104.706
DEMetro_Z 5 40.349 2.6e-13 739.455
DEMetro_Z 8 35.474 1.05e-12 468.053
DEMetro_Z 10 59.012 3.26e-15 261.211
DEMetro_Z 12 56.797 5.71e-15 403.975
DEMetro_Z 15 61.521 1.31e-15 159.035
DEMetro_Z 18 53.584 8.02e-15 179.068
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 40.653 2.42e-13 11.735
DEMetro_Z_vs_SMC 1 35.802 9.71e-13 10.335
DEMetro_Z_vs_SMC 2 59.367 3.83e-15 17.138
DEMetro_Z_vs_SMC 3 57.639 5.29e-15 16.639
DEMetro_Z_vs_SMC 4 60.243 3.26e-15 17.391
DEMetro_Z_vs_SMC 5 54.313 1.02e-14 15.679
HMC_vs_Metro 0 -1.675 0.122 -0.484
HMC_vs_Metro 1 3.530 0.00472 1.019
HMC_vs_Metro 2 5.738 0.000131 1.656
HMC_vs_Metro 3 1.337 0.208 0.386
HMC_vs_Metro 4 0.453 0.66 0.131
HMC_vs_Metro 5 0.406 0.692 0.117
Metro_vs_DEMetro_Z 0 -38.981 3.84e-13 -11.253
Metro_vs_DEMetro_Z 1 -31.771 3.57e-12 -9.172
Metro_vs_DEMetro_Z 2 -15.596 7.56e-09 -4.502
Metro_vs_DEMetro_Z 3 -21.917 2e-10 -6.327
Metro_vs_DEMetro_Z 4 -28.127 1.34e-11 -8.120
Metro_vs_DEMetro_Z 5 -21.523 2.43e-10 -6.213
HMC_vs_SMC 0 2.866 0.0153 0.827
HMC_vs_SMC 1 4.948 0.000437 1.428
HMC_vs_SMC 2 69.873 6.41e-16 20.171
HMC_vs_SMC 3 83.413 9.16e-17 24.079
HMC_vs_SMC 4 78.852 1.7e-16 22.762
HMC_vs_SMC 5 118.318 1.97e-18 34.156
Metro_vs_SMC 0 5.633 0.000153 1.626
Metro_vs_SMC 1 4.816 0.000539 1.390
Metro_vs_SMC 2 3.281 0.00732 0.947
Metro_vs_SMC 3 25.906 3.28e-11 7.478
Metro_vs_SMC 4 135.435 4.45e-19 39.097
Metro_vs_SMC 5 126.859 9.14e-19 36.621
HMC_vs_DEMetro_Z 0 -42.391 1.53e-13 -12.237
HMC_vs_DEMetro_Z 1 -16.774 3.5e-09 -4.842
HMC_vs_DEMetro_Z 2 -31.362 4.11e-12 -9.054
HMC_vs_DEMetro_Z 3 -27.009 2.09e-11 -7.797
HMC_vs_DEMetro_Z 4 -32.383 2.9e-12 -9.348
HMC_vs_DEMetro_Z 5 -20.472 4.16e-10 -5.910
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.020 0.013 0.001 5.374
HMC 8 0.204 0.013 0.002 94.721
HMC 10 0.405 0.013 0.004 111.862
HMC 12 0.452 0.013 0.002 195.891
HMC 15 0.510 0.013 0.006 87.575
HMC 18 0.537 0.014 0.005 105.146
SMC 5 0.014 0.013 0.001 0.790
SMC 8 0.014 0.013 0.002 0.457
SMC 10 0.014 0.013 0.004 0.360
SMC 12 0.016 0.013 0.002 1.053
SMC 15 0.013 0.013 0.006 0.083
SMC 18 0.014 0.014 0.005 -0.045
Metro 5 0.024 0.013 0.001 8.798
Metro 8 0.068 0.013 0.002 27.114
Metro 10 0.152 0.013 0.004 39.689
Metro 12 0.431 0.013 0.002 186.618
Metro 15 0.508 0.013 0.006 87.127
Metro 18 0.535 0.014 0.005 104.706
DEMetro_Z 5 0.919 0.013 0.001 739.455
DEMetro_Z 8 0.958 0.013 0.002 468.053
DEMetro_Z 10 0.929 0.013 0.004 261.211
DEMetro_Z 12 0.918 0.013 0.002 403.975
DEMetro_Z 15 0.916 0.013 0.006 159.035
DEMetro_Z 18 0.905 0.014 0.005 179.068
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
Forest & Ridge Plots
Pooled
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
12 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
18 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
12 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
18 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
5
8
10
12
15
18
Chain
5
8
10
12
15
18

Varying_Mode_Distance_with_high_Correlation (Mixture, mm, 12 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 2.966 0.0128 27.607
HMC 8 7.968 6.51e-06 40.163
HMC 10 3.947 0.00227 33.381
HMC 12 5.472 0.000192 42.519
HMC 15 3.945 0.00229 47.699
HMC 18 3.991 0.00207 14.533
SMC 5 0.460 0.65 0.206
SMC 8 0.150 0.882 0.078
SMC 10 2.146 0.0435 0.960
SMC 12 0.048 0.962 0.018
SMC 15 0.007 0.994 0.003
SMC 18 0.148 0.884 0.054
Metro 5 5.772 0.000123 48.150
Metro 8 5.591 0.000161 43.416
Metro 10 3.515 0.00484 44.409
Metro 12 4.947 0.000434 36.972
Metro 15 4.947 0.000435 48.246
Metro 18 3.925 0.00232 14.134
DEMetro_Z 5 3.694 0.00353 34.497
DEMetro_Z 8 4.514 0.000871 28.034
DEMetro_Z 10 3.521 0.00478 52.959
DEMetro_Z 12 5.519 0.000176 26.363
DEMetro_Z 15 4.171 0.00156 49.256
DEMetro_Z 18 4.759 0.000579 22.753
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -0.551 0.593 -0.159
HMC_vs_DEMetro_Z 1 1.546 0.15 0.446
HMC_vs_DEMetro_Z 2 -1.239 0.241 -0.358
HMC_vs_DEMetro_Z 3 2.386 0.0361 0.689
HMC_vs_DEMetro_Z 4 -0.092 0.928 -0.027
HMC_vs_DEMetro_Z 5 -2.296 0.0423 -0.663
Metro_vs_SMC 0 5.719 0.000134 1.651
Metro_vs_SMC 1 5.399 0.000217 1.559
Metro_vs_SMC 2 3.406 0.00587 0.983
Metro_vs_SMC 3 4.985 0.000412 1.439
Metro_vs_SMC 4 4.920 0.000457 1.420
Metro_vs_SMC 5 3.804 0.00292 1.098
Metro_vs_DEMetro_Z 0 1.181 0.262 0.341
Metro_vs_DEMetro_Z 1 1.472 0.169 0.425
Metro_vs_DEMetro_Z 2 -0.824 0.428 -0.238
Metro_vs_DEMetro_Z 3 1.325 0.212 0.383
Metro_vs_DEMetro_Z 4 -0.059 0.954 -0.017
Metro_vs_DEMetro_Z 5 -1.870 0.0884 -0.540
HMC_vs_Metro 0 -1.342 0.207 -0.387
HMC_vs_Metro 1 -0.361 0.725 -0.104
HMC_vs_Metro 2 -0.809 0.436 -0.234
HMC_vs_Metro 3 0.681 0.51 0.197
HMC_vs_Metro 4 -0.053 0.958 -0.015
HMC_vs_Metro 5 0.136 0.894 0.039
HMC_vs_SMC 0 2.954 0.0131 0.853
HMC_vs_SMC 1 8.063 6.06e-06 2.328
HMC_vs_SMC 2 3.798 0.00295 1.096
HMC_vs_SMC 3 5.576 0.000166 1.610
HMC_vs_SMC 4 3.928 0.00236 1.134
HMC_vs_SMC 5 3.849 0.0027 1.111
DEMetro_Z_vs_SMC 0 3.726 0.00335 1.076
DEMetro_Z_vs_SMC 1 4.481 0.000931 1.293
DEMetro_Z_vs_SMC 2 3.443 0.00549 0.994
DEMetro_Z_vs_SMC 3 5.631 0.000153 1.625
DEMetro_Z_vs_SMC 4 4.136 0.00165 1.194
DEMetro_Z_vs_SMC 5 4.665 0.000688 1.347
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.526 0.034 0.018 27.607
HMC 8 1.428 0.062 0.034 40.163
HMC 10 1.043 0.036 0.030 33.381
HMC 12 2.303 0.063 0.053 42.519
HMC 15 2.214 0.090 0.045 47.699
HMC 18 1.934 0.107 0.126 14.533
SMC 5 0.038 0.034 0.018 0.206
SMC 8 0.065 0.062 0.034 0.078
SMC 10 0.065 0.036 0.030 0.960
SMC 12 0.064 0.063 0.053 0.018
SMC 15 0.090 0.090 0.045 0.003
SMC 18 0.114 0.107 0.126 0.054
Metro 5 0.892 0.034 0.018 48.150
Metro 8 1.539 0.062 0.034 43.416
Metro 10 1.375 0.036 0.030 44.409
Metro 12 2.011 0.063 0.053 36.972
Metro 15 2.238 0.090 0.045 48.246
Metro 18 1.884 0.107 0.126 14.134
DEMetro_Z 5 0.649 0.034 0.018 34.497
DEMetro_Z 8 1.015 0.062 0.034 28.034
DEMetro_Z 10 1.633 0.036 0.030 52.959
DEMetro_Z 12 1.452 0.063 0.053 26.363
DEMetro_Z 15 2.283 0.090 0.045 49.256
DEMetro_Z 18 2.968 0.107 0.126 22.753
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 2.264 0.0447 16.427
HMC 8 4.286 0.00128 40.896
HMC 10 4.148 0.00162 44.075
HMC 12 3.642 0.00388 116.792
HMC 15 2.868 0.0153 89.305
HMC 18 4.038 0.00195 68.199
SMC 5 -0.226 0.823 -0.094
SMC 8 1.311 0.203 0.511
SMC 10 -0.578 0.569 -0.219
SMC 12 1.011 0.323 0.396
SMC 15 -0.616 0.544 -0.245
SMC 18 1.196 0.245 0.580
Metro 5 3.331 0.00668 27.812
Metro 8 3.646 0.00385 56.023
Metro 10 2.733 0.0195 84.207
Metro 12 3.301 0.00706 95.351
Metro 15 3.429 0.00563 77.961
Metro 18 4.276 0.00131 70.837
DEMetro_Z 5 2.333 0.0396 19.889
DEMetro_Z 8 3.543 0.00459 26.399
DEMetro_Z 10 2.857 0.0156 115.493
DEMetro_Z 12 4.510 0.000883 42.937
DEMetro_Z 15 2.904 0.0144 90.031
DEMetro_Z 18 3.158 0.00911 144.865
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 2.230 0.0476 0.644
HMC_vs_SMC 1 4.196 0.0015 1.211
HMC_vs_SMC 2 4.145 0.00163 1.196
HMC_vs_SMC 3 3.638 0.0039 1.050
HMC_vs_SMC 4 2.875 0.0151 0.830
HMC_vs_SMC 5 4.033 0.00197 1.164
Metro_vs_DEMetro_Z 0 0.658 0.524 0.190
Metro_vs_DEMetro_Z 1 1.688 0.119 0.487
Metro_vs_DEMetro_Z 2 -1.109 0.291 -0.320
Metro_vs_DEMetro_Z 3 2.019 0.0685 0.583
Metro_vs_DEMetro_Z 4 -0.290 0.777 -0.084
Metro_vs_DEMetro_Z 5 -1.808 0.0981 -0.522
HMC_vs_Metro 0 -0.854 0.411 -0.247
HMC_vs_Metro 1 -0.798 0.442 -0.230
HMC_vs_Metro 2 -1.372 0.197 -0.396
HMC_vs_Metro 3 0.638 0.536 0.184
HMC_vs_Metro 4 0.497 0.629 0.144
HMC_vs_Metro 5 -0.194 0.85 -0.056
HMC_vs_DEMetro_Z 0 -0.298 0.772 -0.086
HMC_vs_DEMetro_Z 1 1.233 0.243 0.356
HMC_vs_DEMetro_Z 2 -1.819 0.0962 -0.525
HMC_vs_DEMetro_Z 3 2.497 0.0297 0.721
HMC_vs_DEMetro_Z 4 -0.015 0.988 -0.004
HMC_vs_DEMetro_Z 5 -1.952 0.0768 -0.564
Metro_vs_SMC 0 3.371 0.00624 0.973
Metro_vs_SMC 1 3.629 0.00397 1.048
Metro_vs_SMC 2 2.735 0.0194 0.789
Metro_vs_SMC 3 3.295 0.00714 0.951
Metro_vs_SMC 4 3.433 0.0056 0.991
Metro_vs_SMC 5 4.244 0.00138 1.225
DEMetro_Z_vs_SMC 0 2.361 0.0378 0.682
DEMetro_Z_vs_SMC 1 3.432 0.0056 0.991
DEMetro_Z_vs_SMC 2 2.858 0.0156 0.825
DEMetro_Z_vs_SMC 3 4.466 0.000954 1.289
DEMetro_Z_vs_SMC 4 2.902 0.0144 0.838
DEMetro_Z_vs_SMC 5 3.145 0.00933 0.908
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.877 0.082 0.048 16.427
HMC 8 3.317 0.088 0.079 40.896
HMC 10 2.660 0.101 0.058 44.075
HMC 12 10.092 0.102 0.086 116.792
HMC 15 11.692 0.187 0.129 89.305
HMC 18 8.520 0.196 0.122 68.199
SMC 5 0.077 0.082 0.048 -0.094
SMC 8 0.128 0.088 0.079 0.511
SMC 10 0.088 0.101 0.058 -0.219
SMC 12 0.136 0.102 0.086 0.396
SMC 15 0.155 0.187 0.129 -0.245
SMC 18 0.266 0.196 0.122 0.580
Metro 5 1.428 0.082 0.048 27.812
Metro 8 4.511 0.088 0.079 56.023
Metro 10 4.990 0.101 0.058 84.207
Metro 12 8.258 0.102 0.086 95.351
Metro 15 10.231 0.187 0.129 77.961
Metro 18 8.842 0.196 0.122 70.837
DEMetro_Z 5 1.045 0.082 0.048 19.889
DEMetro_Z 8 2.172 0.088 0.079 26.399
DEMetro_Z 10 6.806 0.101 0.058 115.493
DEMetro_Z 12 3.775 0.102 0.086 42.937
DEMetro_Z 15 11.786 0.187 0.129 90.031
DEMetro_Z 18 17.878 0.196 0.122 144.865
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 3.020 0.0116 31.501
HMC 8 7.674 9.35e-06 40.456
HMC 10 3.955 0.00225 43.225
HMC 12 5.337 0.000237 44.435
HMC 15 3.996 0.0021 47.971
HMC 18 3.974 0.00214 17.107
SMC 5 -0.299 0.768 -0.135
SMC 8 0.278 0.784 0.122
SMC 10 1.927 0.0682 0.946
SMC 12 -0.239 0.813 -0.086
SMC 15 -0.393 0.698 -0.170
SMC 18 0.283 0.78 0.109
Metro 5 5.693 0.000139 54.279
Metro 8 5.612 0.000156 43.467
Metro 10 3.667 0.00371 55.313
Metro 12 4.846 0.000511 38.778
Metro 15 4.998 0.000402 50.459
Metro 18 4.140 0.00161 16.676
DEMetro_Z 5 3.620 0.00402 39.568
DEMetro_Z 8 4.622 0.000729 28.688
DEMetro_Z 10 3.539 0.00464 66.304
DEMetro_Z 12 5.581 0.000161 28.610
DEMetro_Z 15 4.249 0.00136 50.791
DEMetro_Z 18 4.429 0.001 27.331
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 1.070 0.307 0.309
Metro_vs_DEMetro_Z 1 1.470 0.17 0.424
Metro_vs_DEMetro_Z 2 -0.826 0.426 -0.238
Metro_vs_DEMetro_Z 3 1.208 0.252 0.349
Metro_vs_DEMetro_Z 4 -0.019 0.985 -0.006
Metro_vs_DEMetro_Z 5 -1.834 0.0938 -0.529
DEMetro_Z_vs_SMC 0 3.682 0.00361 1.063
DEMetro_Z_vs_SMC 1 4.555 0.000823 1.315
DEMetro_Z_vs_SMC 2 3.487 0.00508 1.007
DEMetro_Z_vs_SMC 3 5.675 0.000143 1.638
DEMetro_Z_vs_SMC 4 4.235 0.0014 1.222
DEMetro_Z_vs_SMC 5 4.348 0.00116 1.255
HMC_vs_DEMetro_Z 0 -0.592 0.566 -0.171
HMC_vs_DEMetro_Z 1 1.506 0.16 0.435
HMC_vs_DEMetro_Z 2 -1.185 0.261 -0.342
HMC_vs_DEMetro_Z 3 2.093 0.0603 0.604
HMC_vs_DEMetro_Z 4 -0.166 0.871 -0.048
HMC_vs_DEMetro_Z 5 -2.158 0.0539 -0.623
HMC_vs_Metro 0 -1.299 0.22 -0.375
HMC_vs_Metro 1 -0.321 0.754 -0.093
HMC_vs_Metro 2 -0.734 0.478 -0.212
HMC_vs_Metro 3 0.635 0.539 0.183
HMC_vs_Metro 4 -0.240 0.814 -0.069
HMC_vs_Metro 5 0.128 0.901 0.037
HMC_vs_SMC 0 3.040 0.0112 0.878
HMC_vs_SMC 1 7.736 8.97e-06 2.233
HMC_vs_SMC 2 3.845 0.00272 1.110
HMC_vs_SMC 3 5.438 0.000204 1.570
HMC_vs_SMC 4 3.990 0.00212 1.152
HMC_vs_SMC 5 3.832 0.00279 1.106
Metro_vs_SMC 0 5.702 0.000138 1.646
Metro_vs_SMC 1 5.455 0.000199 1.575
Metro_vs_SMC 2 3.581 0.00431 1.034
Metro_vs_SMC 3 4.898 0.000473 1.414
Metro_vs_SMC 4 4.979 0.000416 1.437
Metro_vs_SMC 5 4.002 0.00208 1.155
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.486 0.050 0.014 31.501
HMC 8 1.296 0.070 0.030 40.456
HMC 10 0.974 0.052 0.021 43.225
HMC 12 2.103 0.075 0.046 44.435
HMC 15 1.966 0.103 0.039 47.971
HMC 18 1.773 0.114 0.097 17.107
SMC 5 0.048 0.050 0.014 -0.135
SMC 8 0.073 0.070 0.030 0.122
SMC 10 0.072 0.052 0.021 0.946
SMC 12 0.071 0.075 0.046 -0.086
SMC 15 0.097 0.103 0.039 -0.170
SMC 18 0.125 0.114 0.097 0.109
Metro 5 0.801 0.050 0.014 54.279
Metro 8 1.387 0.070 0.030 43.467
Metro 10 1.232 0.052 0.021 55.313
Metro 12 1.845 0.075 0.046 38.778
Metro 15 2.063 0.103 0.039 50.459
Metro 18 1.732 0.114 0.097 16.676
DEMetro_Z 5 0.598 0.050 0.014 39.568
DEMetro_Z 8 0.939 0.070 0.030 28.688
DEMetro_Z 10 1.466 0.052 0.021 66.304
DEMetro_Z 12 1.381 0.075 0.046 28.610
DEMetro_Z 15 2.076 0.103 0.039 50.791
DEMetro_Z 18 2.765 0.114 0.097 27.331
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 2.939 0.0134 30.824
HMC 8 7.993 6.37e-06 44.238
HMC 10 3.962 0.00222 43.382
HMC 12 5.666 0.000144 47.080
HMC 15 4.050 0.00191 60.356
HMC 18 3.992 0.00208 18.660
SMC 5 -0.099 0.922 -0.042
SMC 8 0.387 0.703 0.175
SMC 10 2.089 0.0493 0.987
SMC 12 -0.105 0.918 -0.037
SMC 15 -0.203 0.841 -0.092
SMC 18 0.268 0.792 0.103
Metro 5 5.332 0.000239 53.222
Metro 8 5.555 0.00017 47.437
Metro 10 3.719 0.00338 57.580
Metro 12 5.051 0.000368 40.300
Metro 15 5.051 0.00037 61.198
Metro 18 4.122 0.00167 19.046
DEMetro_Z 5 3.523 0.00476 39.916
DEMetro_Z 8 4.510 0.000878 30.827
DEMetro_Z 10 3.535 0.00467 65.750
DEMetro_Z 12 5.495 0.000184 30.064
DEMetro_Z 15 4.377 0.0011 61.755
DEMetro_Z 18 4.872 0.000487 28.965
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 3.561 0.00446 1.028
DEMetro_Z_vs_SMC 1 4.470 0.000947 1.290
DEMetro_Z_vs_SMC 2 3.476 0.00518 1.003
DEMetro_Z_vs_SMC 3 5.583 0.000164 1.612
DEMetro_Z_vs_SMC 4 4.356 0.00114 1.257
DEMetro_Z_vs_SMC 5 4.776 0.000575 1.379
HMC_vs_Metro 0 -1.276 0.228 -0.368
HMC_vs_Metro 1 -0.315 0.758 -0.091
HMC_vs_Metro 2 -0.846 0.416 -0.244
HMC_vs_Metro 3 0.779 0.453 0.225
HMC_vs_Metro 4 -0.064 0.95 -0.019
HMC_vs_Metro 5 -0.108 0.916 -0.031
Metro_vs_DEMetro_Z 0 0.969 0.354 0.280
Metro_vs_DEMetro_Z 1 1.415 0.185 0.409
Metro_vs_DEMetro_Z 2 -0.621 0.547 -0.179
Metro_vs_DEMetro_Z 3 1.183 0.262 0.342
Metro_vs_DEMetro_Z 4 -0.027 0.979 -0.008
Metro_vs_DEMetro_Z 5 -1.741 0.11 -0.503
HMC_vs_SMC 0 2.932 0.0136 0.846
HMC_vs_SMC 1 8.025 6.34e-06 2.317
HMC_vs_SMC 2 3.837 0.00276 1.108
HMC_vs_SMC 3 5.750 0.000128 1.660
HMC_vs_SMC 4 4.037 0.00196 1.165
HMC_vs_SMC 5 3.842 0.00273 1.109
Metro_vs_SMC 0 5.349 0.000234 1.544
Metro_vs_SMC 1 5.402 0.000216 1.559
Metro_vs_SMC 2 3.635 0.00392 1.049
Metro_vs_SMC 3 5.089 0.00035 1.469
Metro_vs_SMC 4 5.044 0.000376 1.456
Metro_vs_SMC 5 4.001 0.00208 1.155
HMC_vs_DEMetro_Z 0 -0.611 0.554 -0.176
HMC_vs_DEMetro_Z 1 1.560 0.147 0.450
HMC_vs_DEMetro_Z 2 -1.141 0.278 -0.329
HMC_vs_DEMetro_Z 3 2.337 0.0394 0.675
HMC_vs_DEMetro_Z 4 -0.069 0.946 -0.020
HMC_vs_DEMetro_Z 5 -2.290 0.0428 -0.661
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.156 0.013 0.005 30.824
HMC 8 0.311 0.013 0.007 44.238
HMC 10 0.193 0.007 0.004 43.382
HMC 12 0.350 0.009 0.007 47.080
HMC 15 0.272 0.010 0.004 60.356
HMC 18 0.199 0.010 0.010 18.660
SMC 5 0.013 0.013 0.005 -0.042
SMC 8 0.014 0.013 0.007 0.175
SMC 10 0.011 0.007 0.004 0.987
SMC 12 0.009 0.009 0.007 -0.037
SMC 15 0.010 0.010 0.004 -0.092
SMC 18 0.011 0.010 0.010 0.103
Metro 5 0.260 0.013 0.005 53.222
Metro 8 0.333 0.013 0.007 47.437
Metro 10 0.254 0.007 0.004 57.580
Metro 12 0.301 0.009 0.007 40.300
Metro 15 0.276 0.010 0.004 61.198
Metro 18 0.202 0.010 0.010 19.046
DEMetro_Z 5 0.198 0.013 0.005 39.916
DEMetro_Z 8 0.221 0.013 0.007 30.827
DEMetro_Z 10 0.289 0.007 0.004 65.750
DEMetro_Z 12 0.227 0.009 0.007 30.064
DEMetro_Z 15 0.278 0.010 0.004 61.755
DEMetro_Z 18 0.303 0.010 0.010 28.965
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 138.598 3.45e-25 96.869
HMC 8 137.242 1.06e-27 81.064
HMC 10 197.817 2.09e-30 117.075
HMC 12 169.349 4.84e-34 79.724
HMC 15 198.648 1.72e-30 117.248
HMC 18 115.503 6.99e-32 49.587
SMC 5 -0.436 0.667 -0.174
SMC 8 0.326 0.748 0.170
SMC 10 1.904 0.0709 0.905
SMC 12 0.595 0.558 0.212
SMC 15 0.479 0.637 0.203
SMC 18 -0.639 0.533 -0.197
Metro 5 5.061 0.000364 55.186
Metro 8 124.642 1.75e-25 80.895
Metro 10 132.262 1.75e-22 117.630
Metro 12 158.892 3.84e-32 79.760
Metro 15 238.754 5.87e-36 118.234
Metro 18 130.077 1.11e-32 49.602
DEMetro_Z 5 4.356 0.00114 59.925
DEMetro_Z 8 7.437 1.28e-05 67.148
DEMetro_Z 10 161.319 9.13e-26 116.536
DEMetro_Z 12 149.952 1.16e-30 78.874
DEMetro_Z 15 209.535 7.03e-32 118.010
DEMetro_Z 18 115.919 6.29e-32 49.696
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 2.708 0.0204 0.782
HMC_vs_DEMetro_Z 1 1.526 0.155 0.440
HMC_vs_DEMetro_Z 2 0.678 0.512 0.196
HMC_vs_DEMetro_Z 3 1.352 0.203 0.390
HMC_vs_DEMetro_Z 4 -1.227 0.245 -0.354
HMC_vs_DEMetro_Z 5 -0.312 0.761 -0.090
Metro_vs_SMC 0 5.028 0.000385 1.451
Metro_vs_SMC 1 90.236 3.86e-17 26.049
Metro_vs_SMC 2 126.758 9.22e-19 36.592
Metro_vs_SMC 3 220.509 2.09e-21 63.655
Metro_vs_SMC 4 231.065 1.25e-21 66.703
Metro_vs_SMC 5 181.820 1.75e-20 52.487
Metro_vs_DEMetro_Z 0 -0.243 0.813 -0.070
Metro_vs_DEMetro_Z 1 1.517 0.158 0.438
Metro_vs_DEMetro_Z 2 1.116 0.288 0.322
Metro_vs_DEMetro_Z 3 1.187 0.26 0.343
Metro_vs_DEMetro_Z 4 0.444 0.665 0.128
Metro_vs_DEMetro_Z 5 -0.316 0.758 -0.091
HMC_vs_Metro 0 3.750 0.00321 1.083
HMC_vs_Metro 1 0.268 0.794 0.077
HMC_vs_Metro 2 -0.546 0.596 -0.158
HMC_vs_Metro 3 -0.102 0.92 -0.030
HMC_vs_Metro 4 -2.484 0.0303 -0.717
HMC_vs_Metro 5 -0.085 0.934 -0.024
HMC_vs_SMC 0 136.925 3.95e-19 39.527
HMC_vs_SMC 1 98.957 1.4e-17 28.566
HMC_vs_SMC 2 201.189 5.74e-21 58.078
HMC_vs_SMC 3 257.620 3.78e-22 74.368
HMC_vs_SMC 4 206.033 4.42e-21 59.477
HMC_vs_SMC 5 143.878 2.29e-19 41.534
DEMetro_Z_vs_SMC 0 4.376 0.00111 1.263
DEMetro_Z_vs_SMC 1 7.354 1.44e-05 2.123
DEMetro_Z_vs_SMC 2 177.861 2.23e-20 51.344
DEMetro_Z_vs_SMC 3 155.956 9.44e-20 45.021
DEMetro_Z_vs_SMC 4 179.952 1.96e-20 51.948
DEMetro_Z_vs_SMC 5 140.099 3.07e-19 40.443
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 1.760 0.034 0.018 96.869
HMC 8 2.819 0.062 0.034 81.064
HMC 10 3.567 0.036 0.030 117.075
HMC 12 4.262 0.063 0.053 79.724
HMC 15 5.310 0.090 0.045 117.248
HMC 18 6.342 0.107 0.126 49.587
SMC 5 0.031 0.034 0.018 -0.174
SMC 8 0.068 0.062 0.034 0.170
SMC 10 0.063 0.036 0.030 0.905
SMC 12 0.074 0.063 0.053 0.212
SMC 15 0.099 0.090 0.045 0.203
SMC 18 0.082 0.107 0.126 -0.197
Metro 5 1.017 0.034 0.018 55.186
Metro 8 2.813 0.062 0.034 80.895
Metro 10 3.583 0.036 0.030 117.630
Metro 12 4.264 0.063 0.053 79.760
Metro 15 5.354 0.090 0.045 118.234
Metro 18 6.344 0.107 0.126 49.602
DEMetro_Z 5 1.102 0.034 0.018 59.925
DEMetro_Z 8 2.346 0.062 0.034 67.148
DEMetro_Z 10 3.550 0.036 0.030 116.536
DEMetro_Z 12 4.218 0.063 0.053 78.874
DEMetro_Z 15 5.344 0.090 0.045 118.010
DEMetro_Z 18 6.355 0.107 0.126 49.696
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 187.014 1.22e-34 89.281
HMC 8 382.847 9.18e-42 141.272
HMC 10 468.154 7.76e-35 302.460
HMC 12 495.662 4.64e-37 296.043
HMC 15 767.288 3.87e-50 307.419
HMC 18 1058.120 2.78e-52 467.556
SMC 5 -0.570 0.575 -0.210
SMC 8 0.153 0.88 0.057
SMC 10 0.195 0.847 0.080
SMC 12 1.094 0.287 0.550
SMC 15 0.488 0.631 0.171
SMC 18 0.664 0.514 0.319
Metro 5 4.063 0.00187 41.817
Metro 8 306.324 9.49e-40 141.877
Metro 10 468.775 6.99e-35 302.347
Metro 12 497.398 3.63e-37 296.125
Metro 15 676.422 1.89e-47 307.450
Metro 18 905.063 4.36e-46 467.624
DEMetro_Z 5 4.032 0.00197 53.078
DEMetro_Z 8 7.355 1.43e-05 115.470
DEMetro_Z 10 451.445 7.93e-34 302.723
DEMetro_Z 12 552.403 7.08e-41 295.924
DEMetro_Z 15 715.816 3.85e-49 307.381
DEMetro_Z 18 1016.327 7.25e-51 467.470
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 209.543 3.67e-21 60.490
HMC_vs_SMC 1 342.574 1.65e-23 98.892
HMC_vs_SMC 2 408.453 2.38e-24 117.910
HMC_vs_SMC 3 344.941 1.53e-23 99.576
HMC_vs_SMC 4 828.011 1e-27 239.026
HMC_vs_SMC 5 1155.207 2.57e-29 333.480
Metro_vs_DEMetro_Z 0 -0.606 0.557 -0.175
Metro_vs_DEMetro_Z 1 1.693 0.119 0.489
Metro_vs_DEMetro_Z 2 -0.922 0.376 -0.266
Metro_vs_DEMetro_Z 3 0.792 0.445 0.229
Metro_vs_DEMetro_Z 4 0.341 0.74 0.098
Metro_vs_DEMetro_Z 5 0.551 0.593 0.159
HMC_vs_Metro 0 4.553 0.000826 1.314
HMC_vs_Metro 1 -2.347 0.0387 -0.677
HMC_vs_Metro 2 0.282 0.783 0.081
HMC_vs_Metro 3 -0.379 0.712 -0.109
HMC_vs_Metro 4 -0.167 0.871 -0.048
HMC_vs_Metro 5 -0.298 0.772 -0.086
HMC_vs_DEMetro_Z 0 2.801 0.0172 0.809
HMC_vs_DEMetro_Z 1 1.645 0.128 0.475
HMC_vs_DEMetro_Z 2 -0.962 0.356 -0.278
HMC_vs_DEMetro_Z 3 0.566 0.583 0.163
HMC_vs_DEMetro_Z 4 0.317 0.757 0.092
HMC_vs_DEMetro_Z 5 0.736 0.477 0.213
Metro_vs_SMC 0 4.145 0.00163 1.197
Metro_vs_SMC 1 255.251 4.19e-22 73.685
Metro_vs_SMC 2 405.778 2.56e-24 117.138
Metro_vs_SMC 3 345.618 1.49e-23 99.771
Metro_vs_SMC 4 742.804 3.31e-27 214.429
Metro_vs_SMC 5 1005.076 1.19e-28 290.141
DEMetro_Z_vs_SMC 0 4.046 0.00193 1.168
DEMetro_Z_vs_SMC 1 7.326 1.49e-05 2.115
DEMetro_Z_vs_SMC 2 362.726 8.78e-24 104.710
DEMetro_Z_vs_SMC 3 381.113 5.1e-24 110.018
DEMetro_Z_vs_SMC 4 759.844 2.58e-27 219.348
DEMetro_Z_vs_SMC 5 993.522 1.35e-28 286.805
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 4.405 0.082 0.048 89.281
HMC 8 11.242 0.088 0.079 141.272
HMC 10 17.660 0.101 0.058 302.460
HMC 12 25.424 0.102 0.086 296.043
HMC 15 39.793 0.187 0.129 307.419
HMC 18 57.267 0.196 0.122 467.556
SMC 5 0.072 0.082 0.048 -0.210
SMC 8 0.093 0.088 0.079 0.057
SMC 10 0.106 0.101 0.058 0.080
SMC 12 0.149 0.102 0.086 0.550
SMC 15 0.209 0.187 0.129 0.171
SMC 18 0.235 0.196 0.122 0.319
Metro 5 2.107 0.082 0.048 41.817
Metro 8 11.290 0.088 0.079 141.877
Metro 10 17.654 0.101 0.058 302.347
Metro 12 25.431 0.102 0.086 296.125
Metro 15 39.797 0.187 0.129 307.450
Metro 18 57.275 0.196 0.122 467.624
DEMetro_Z 5 2.652 0.082 0.048 53.078
DEMetro_Z 8 9.205 0.088 0.079 115.470
DEMetro_Z 10 17.675 0.101 0.058 302.723
DEMetro_Z 12 25.414 0.102 0.086 295.924
DEMetro_Z 15 39.788 0.187 0.129 307.381
DEMetro_Z 18 57.256 0.196 0.122 467.470
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 56.130 2.34e-15 112.172
HMC 8 60.328 2.35e-16 80.448
HMC 10 40.122 2.13e-13 149.553
HMC 12 37.066 3.04e-13 79.979
HMC 15 38.014 3.4e-13 115.985
HMC 18 34.979 3.32e-13 57.417
SMC 5 -1.393 0.178 -0.523
SMC 8 0.150 0.882 0.072
SMC 10 1.672 0.11 0.842
SMC 12 0.421 0.679 0.147
SMC 15 -0.062 0.951 -0.025
SMC 18 -0.695 0.498 -0.220
Metro 5 5.029 0.000384 64.126
Metro 8 42.236 5.82e-14 83.063
Metro 10 37.634 4.53e-13 154.093
Metro 12 68.819 1.79e-17 79.169
Metro 15 51.698 7.52e-15 116.301
Metro 18 53.565 2.38e-16 57.478
DEMetro_Z 5 4.394 0.00107 70.757
DEMetro_Z 8 7.271 1.58e-05 65.234
DEMetro_Z 10 53.942 5.96e-15 143.807
DEMetro_Z 12 61.841 1.6e-16 81.203
DEMetro_Z 15 45.654 3.88e-14 121.905
DEMetro_Z 18 45.707 5.2e-15 58.064
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -0.298 0.772 -0.086
Metro_vs_DEMetro_Z 1 1.841 0.0927 0.531
Metro_vs_DEMetro_Z 2 2.528 0.0281 0.730
Metro_vs_DEMetro_Z 3 -1.375 0.196 -0.397
Metro_vs_DEMetro_Z 4 -2.350 0.0385 -0.678
Metro_vs_DEMetro_Z 5 -0.372 0.717 -0.107
DEMetro_Z_vs_SMC 0 4.432 0.00101 1.279
DEMetro_Z_vs_SMC 1 7.209 1.73e-05 2.081
DEMetro_Z_vs_SMC 2 53.530 1.19e-14 15.453
DEMetro_Z_vs_SMC 3 59.628 3.65e-15 17.213
DEMetro_Z_vs_SMC 4 44.571 8.86e-14 12.867
DEMetro_Z_vs_SMC 5 48.028 3.91e-14 13.864
HMC_vs_DEMetro_Z 0 2.659 0.0222 0.768
HMC_vs_DEMetro_Z 1 1.703 0.117 0.492
HMC_vs_DEMetro_Z 2 1.102 0.294 0.318
HMC_vs_DEMetro_Z 3 -0.498 0.628 -0.144
HMC_vs_DEMetro_Z 4 -1.244 0.239 -0.359
HMC_vs_DEMetro_Z 5 -0.322 0.753 -0.093
HMC_vs_Metro 0 3.695 0.00353 1.067
HMC_vs_Metro 1 -1.021 0.329 -0.295
HMC_vs_Metro 2 -0.701 0.498 -0.202
HMC_vs_Metro 3 0.318 0.757 0.092
HMC_vs_Metro 4 -0.071 0.944 -0.021
HMC_vs_Metro 5 -0.033 0.974 -0.009
HMC_vs_SMC 0 53.718 1.15e-14 15.507
HMC_vs_SMC 1 67.993 8.64e-16 19.628
HMC_vs_SMC 2 38.306 4.64e-13 11.058
HMC_vs_SMC 3 37.540 5.79e-13 10.837
HMC_vs_SMC 4 37.341 6.13e-13 10.779
HMC_vs_SMC 5 34.384 1.51e-12 9.926
Metro_vs_SMC 0 5.042 0.000377 1.456
Metro_vs_SMC 1 38.609 4.26e-13 11.145
Metro_vs_SMC 2 36.131 8.79e-13 10.430
Metro_vs_SMC 3 68.274 8.26e-16 19.709
Metro_vs_SMC 4 52.214 1.57e-14 15.073
Metro_vs_SMC 5 57.802 5.13e-15 16.686
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 1.603 0.050 0.014 112.172
HMC 8 2.508 0.070 0.030 80.448
HMC 10 3.241 0.052 0.021 149.553
HMC 12 3.725 0.075 0.046 79.979
HMC 15 4.607 0.103 0.039 115.985
HMC 18 5.683 0.114 0.097 57.417
SMC 5 0.042 0.050 0.014 -0.523
SMC 8 0.072 0.070 0.030 0.072
SMC 10 0.070 0.052 0.021 0.842
SMC 12 0.082 0.075 0.046 0.147
SMC 15 0.102 0.103 0.039 -0.025
SMC 18 0.093 0.114 0.097 -0.220
Metro 5 0.938 0.050 0.014 64.126
Metro 8 2.587 0.070 0.030 83.063
Metro 10 3.338 0.052 0.021 154.093
Metro 12 3.688 0.075 0.046 79.169
Metro 15 4.620 0.103 0.039 116.301
Metro 18 5.689 0.114 0.097 57.478
DEMetro_Z 5 1.030 0.050 0.014 70.757
DEMetro_Z 8 2.046 0.070 0.030 65.234
DEMetro_Z 10 3.118 0.052 0.021 143.807
DEMetro_Z 12 3.781 0.075 0.046 81.203
DEMetro_Z 15 4.837 0.103 0.039 121.905
DEMetro_Z 18 5.746 0.114 0.097 58.064
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 146.715 3.04e-24 114.830
HMC 8 66.898 6.5e-17 88.555
HMC 10 86.498 9.51e-18 145.283
HMC 12 130.369 1.45e-25 85.960
HMC 15 106.048 2.66e-19 141.787
HMC 18 112.906 4e-28 60.022
SMC 5 -1.310 0.204 -0.495
SMC 8 0.177 0.861 0.086
SMC 10 1.555 0.136 0.772
SMC 12 0.588 0.563 0.206
SMC 15 0.997 0.33 0.450
SMC 18 -0.242 0.812 -0.078
Metro 5 4.875 0.000489 61.934
Metro 8 94.274 5.11e-20 90.554
Metro 10 162.731 1.12e-23 145.183
Metro 12 110.952 1.43e-22 86.192
Metro 15 118.478 3.59e-20 145.046
Metro 18 79.674 1.15e-20 60.712
DEMetro_Z 5 4.391 0.00108 70.131
DEMetro_Z 8 7.404 1.34e-05 73.928
DEMetro_Z 10 78.721 3.78e-17 143.702
DEMetro_Z 12 98.183 7.25e-21 85.652
DEMetro_Z 15 91.256 3.54e-18 140.684
DEMetro_Z 18 77.318 2.88e-20 60.369
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 4.421 0.00103 1.276
DEMetro_Z_vs_SMC 1 7.355 1.44e-05 2.123
DEMetro_Z_vs_SMC 2 87.084 5.71e-17 25.139
DEMetro_Z_vs_SMC 3 98.606 1.46e-17 28.465
DEMetro_Z_vs_SMC 4 94.346 2.37e-17 27.235
DEMetro_Z_vs_SMC 5 75.868 2.6e-16 21.901
HMC_vs_Metro 0 4.186 0.00152 1.208
HMC_vs_Metro 1 -1.870 0.0883 -0.540
HMC_vs_Metro 2 0.061 0.953 0.018
HMC_vs_Metro 3 -0.342 0.739 -0.099
HMC_vs_Metro 4 -2.160 0.0537 -0.624
HMC_vs_Metro 5 -1.026 0.327 -0.296
Metro_vs_DEMetro_Z 0 -0.364 0.723 -0.105
Metro_vs_DEMetro_Z 1 1.631 0.131 0.471
Metro_vs_DEMetro_Z 2 0.895 0.39 0.258
Metro_vs_DEMetro_Z 3 0.490 0.634 0.142
Metro_vs_DEMetro_Z 4 3.024 0.0116 0.873
Metro_vs_DEMetro_Z 5 0.386 0.707 0.111
HMC_vs_SMC 0 130.412 6.75e-19 37.647
HMC_vs_SMC 1 60.898 2.9e-15 17.580
HMC_vs_SMC 2 98.614 1.46e-17 28.467
HMC_vs_SMC 3 158.907 7.68e-20 45.873
HMC_vs_SMC 4 115.229 2.63e-18 33.264
HMC_vs_SMC 5 115.117 2.66e-18 33.232
Metro_vs_SMC 0 4.892 0.000478 1.412
Metro_vs_SMC 1 75.569 2.71e-16 21.815
Metro_vs_SMC 2 179.365 2.03e-20 51.778
Metro_vs_SMC 3 138.916 3.37e-19 40.102
Metro_vs_SMC 4 117.716 2.08e-18 33.982
Metro_vs_SMC 5 90.087 3.93e-17 26.006
HMC_vs_DEMetro_Z 0 2.784 0.0178 0.804
HMC_vs_DEMetro_Z 1 1.349 0.204 0.389
HMC_vs_DEMetro_Z 2 0.689 0.505 0.199
HMC_vs_DEMetro_Z 3 0.282 0.783 0.081
HMC_vs_DEMetro_Z 4 0.603 0.559 0.174
HMC_vs_DEMetro_Z 5 -0.544 0.597 -0.157
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.545 0.013 0.005 114.830
HMC 8 0.610 0.013 0.007 88.555
HMC 10 0.630 0.007 0.004 145.283
HMC 12 0.631 0.009 0.007 85.960
HMC 15 0.626 0.010 0.004 141.787
HMC 18 0.616 0.010 0.010 60.022
SMC 5 0.011 0.013 0.005 -0.495
SMC 8 0.013 0.013 0.007 0.086
SMC 10 0.010 0.007 0.004 0.772
SMC 12 0.011 0.009 0.007 0.206
SMC 15 0.012 0.010 0.004 0.450
SMC 18 0.009 0.010 0.010 -0.078
Metro 5 0.300 0.013 0.005 61.934
Metro 8 0.624 0.013 0.007 90.554
Metro 10 0.630 0.007 0.004 145.183
Metro 12 0.633 0.009 0.007 86.192
Metro 15 0.640 0.010 0.004 145.046
Metro 18 0.623 0.010 0.010 60.712
DEMetro_Z 5 0.338 0.013 0.005 70.131
DEMetro_Z 8 0.512 0.013 0.007 73.928
DEMetro_Z 10 0.623 0.007 0.004 143.702
DEMetro_Z 12 0.629 0.009 0.007 85.652
DEMetro_Z 15 0.621 0.010 0.004 140.684
DEMetro_Z 18 0.620 0.010 0.010 60.369
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
12 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
18 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
12 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
18 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
5
8
10
12
15
18
Chain
5
8
10
12
15
18

Varying_Mode_Distance_with_heavy_Tails (Mixture, mm, 12 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 2.067 0.052 1.036
HMC 8 3.930 0.00209 6.369
HMC 10 3.733 0.00265 4.176
HMC 12 3.092 0.00909 3.770
HMC 15 3.966 0.00151 3.578
HMC 18 3.033 0.0111 7.966
SMC 5 4.051 0.00123 3.475
SMC 8 3.029 0.0108 5.080
SMC 10 2.026 0.067 4.931
SMC 12 2.734 0.0161 2.241
SMC 15 2.930 0.00915 1.705
SMC 18 3.808 0.00254 5.614
Metro 5 4.641 0.000356 3.630
Metro 8 1.723 0.112 6.534
Metro 10 2.756 0.0151 2.145
Metro 12 3.458 0.00295 2.045
Metro 15 2.833 0.0101 1.355
Metro 18 2.420 0.0337 7.371
DEMetro_Z 5 4.228 0.000732 3.071
DEMetro_Z 8 4.321 0.00115 11.367
DEMetro_Z 10 3.672 0.00349 8.420
DEMetro_Z 12 2.871 0.0143 4.593
DEMetro_Z 15 3.378 0.00567 5.524
DEMetro_Z 18 3.965 0.00219 20.501
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -2.881 0.0149 -0.832
HMC_vs_DEMetro_Z 1 -1.393 0.191 -0.402
HMC_vs_DEMetro_Z 2 -1.848 0.0917 -0.533
HMC_vs_DEMetro_Z 3 -0.472 0.646 -0.136
HMC_vs_DEMetro_Z 4 -1.137 0.28 -0.328
HMC_vs_DEMetro_Z 5 -1.912 0.0822 -0.552
Metro_vs_SMC 0 0.169 0.869 0.049
Metro_vs_SMC 1 0.329 0.748 0.095
Metro_vs_SMC 2 -1.101 0.294 -0.318
Metro_vs_SMC 3 -0.186 0.856 -0.054
Metro_vs_SMC 4 -0.478 0.642 -0.138
Metro_vs_SMC 5 0.508 0.621 0.147
Metro_vs_DEMetro_Z 0 0.557 0.589 0.161
Metro_vs_DEMetro_Z 1 -1.036 0.323 -0.299
Metro_vs_DEMetro_Z 2 -2.679 0.0215 -0.773
Metro_vs_DEMetro_Z 3 -1.580 0.142 -0.456
Metro_vs_DEMetro_Z 4 -2.686 0.0212 -0.775
Metro_vs_DEMetro_Z 5 -2.130 0.0566 -0.615
HMC_vs_Metro 0 -3.285 0.00727 -0.948
HMC_vs_Metro 1 -0.041 0.968 -0.012
HMC_vs_Metro 2 1.643 0.129 0.474
HMC_vs_Metro 3 1.365 0.199 0.394
HMC_vs_Metro 4 2.924 0.0138 0.844
HMC_vs_Metro 5 0.158 0.877 0.046
HMC_vs_SMC 0 -2.541 0.0275 -0.733
HMC_vs_SMC 1 0.591 0.566 0.171
HMC_vs_SMC 2 -0.275 0.788 -0.080
HMC_vs_SMC 3 1.031 0.325 0.298
HMC_vs_SMC 4 1.551 0.149 0.448
HMC_vs_SMC 5 0.743 0.473 0.214
DEMetro_Z_vs_SMC 0 -0.383 0.709 -0.110
DEMetro_Z_vs_SMC 1 1.878 0.0871 0.542
DEMetro_Z_vs_SMC 2 1.299 0.221 0.375
DEMetro_Z_vs_SMC 3 1.180 0.263 0.341
DEMetro_Z_vs_SMC 4 2.236 0.047 0.645
DEMetro_Z_vs_SMC 5 2.814 0.0168 0.812
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.084 0.049 0.034 1.036
HMC 8 0.239 0.059 0.028 6.369
HMC 10 0.307 0.098 0.050 4.176
HMC 12 0.476 0.134 0.091 3.770
HMC 15 0.804 0.153 0.182 3.578
HMC 18 0.838 0.168 0.084 7.966
SMC 5 0.167 0.049 0.034 3.475
SMC 8 0.203 0.059 0.028 5.080
SMC 10 0.345 0.098 0.050 4.931
SMC 12 0.338 0.134 0.091 2.241
SMC 15 0.463 0.153 0.182 1.705
SMC 18 0.640 0.168 0.084 5.614
Metro 5 0.172 0.049 0.034 3.630
Metro 8 0.244 0.059 0.028 6.534
Metro 10 0.205 0.098 0.050 2.145
Metro 12 0.320 0.134 0.091 2.045
Metro 15 0.400 0.153 0.182 1.355
Metro 18 0.788 0.168 0.084 7.371
DEMetro_Z 5 0.153 0.049 0.034 3.071
DEMetro_Z 8 0.381 0.059 0.028 11.367
DEMetro_Z 10 0.520 0.098 0.050 8.420
DEMetro_Z 12 0.551 0.134 0.091 4.593
DEMetro_Z 15 1.157 0.153 0.182 5.524
DEMetro_Z 18 1.893 0.168 0.084 20.501
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 -1.522 0.156 -0.440
HMC 8 -0.017 0.987 -0.009
HMC 10 -1.390 0.187 -0.426
HMC 12 0.797 0.436 0.482
HMC 15 -0.617 0.547 -0.189
HMC 18 1.287 0.224 3.288
SMC 5 -1.454 0.173 -0.421
SMC 8 -0.503 0.622 -0.162
SMC 10 0.021 0.983 0.007
SMC 12 0.780 0.446 0.254
SMC 15 -0.614 0.549 -0.188
SMC 18 0.887 0.393 2.189
Metro 5 -1.493 0.163 -0.432
Metro 8 0.483 0.637 0.452
Metro 10 -1.014 0.328 -0.311
Metro 12 0.637 0.531 0.223
Metro 15 -0.604 0.556 -0.184
Metro 18 0.951 0.362 2.430
DEMetro_Z 5 -1.454 0.174 -0.421
DEMetro_Z 8 -1.317 0.208 -0.413
DEMetro_Z 10 -0.858 0.406 -0.262
DEMetro_Z 12 0.460 0.653 0.139
DEMetro_Z 15 -0.593 0.563 -0.181
DEMetro_Z 18 1.312 0.215 3.309
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -1.068 0.308 -0.308
HMC_vs_SMC 1 0.330 0.748 0.095
HMC_vs_SMC 2 -3.012 0.0118 -0.869
HMC_vs_SMC 3 0.413 0.688 0.119
HMC_vs_SMC 4 -0.470 0.647 -0.136
HMC_vs_SMC 5 1.241 0.24 0.358
Metro_vs_DEMetro_Z 0 -0.411 0.689 -0.119
Metro_vs_DEMetro_Z 1 0.982 0.347 0.284
Metro_vs_DEMetro_Z 2 -0.993 0.342 -0.287
Metro_vs_DEMetro_Z 3 0.367 0.72 0.106
Metro_vs_DEMetro_Z 4 -0.942 0.366 -0.272
Metro_vs_DEMetro_Z 5 -1.930 0.0798 -0.557
HMC_vs_Metro 0 -0.344 0.737 -0.099
HMC_vs_Metro 1 -0.460 0.655 -0.133
HMC_vs_Metro 2 -2.029 0.0674 -0.586
HMC_vs_Metro 3 0.511 0.619 0.148
HMC_vs_Metro 4 -1.915 0.0819 -0.553
HMC_vs_Metro 5 0.991 0.343 0.286
HMC_vs_DEMetro_Z 0 -2.422 0.0339 -0.699
HMC_vs_DEMetro_Z 1 1.070 0.308 0.309
HMC_vs_DEMetro_Z 2 -2.856 0.0156 -0.824
HMC_vs_DEMetro_Z 3 0.666 0.519 0.192
HMC_vs_DEMetro_Z 4 -2.781 0.0179 -0.803
HMC_vs_DEMetro_Z 5 -0.022 0.983 -0.006
Metro_vs_SMC 0 -0.338 0.741 -0.098
Metro_vs_SMC 1 0.669 0.517 0.193
Metro_vs_SMC 2 -2.017 0.0688 -0.582
Metro_vs_SMC 3 -0.137 0.894 -0.039
Metro_vs_SMC 4 1.282 0.226 0.370
Metro_vs_SMC 5 1.017 0.331 0.293
DEMetro_Z_vs_SMC 0 0.025 0.981 0.007
DEMetro_Z_vs_SMC 1 -1.324 0.212 -0.382
DEMetro_Z_vs_SMC 2 -1.799 0.0994 -0.519
DEMetro_Z_vs_SMC 3 -0.532 0.606 -0.153
DEMetro_Z_vs_SMC 4 1.745 0.109 0.504
DEMetro_Z_vs_SMC 5 2.307 0.0415 0.666
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 3.355 25.768 50.962 -0.440
HMC 8 7.299 7.363 7.280 -0.009
HMC 10 3.012 7.024 9.415 -0.426
HMC 12 8.712 4.533 8.662 0.482
HMC 15 70.681 192.081 643.882 -0.189
HMC 18 27.558 6.741 6.332 3.288
SMC 5 4.312 25.768 50.962 -0.421
SMC 8 6.187 7.363 7.280 -0.162
SMC 10 7.087 7.024 9.415 0.007
SMC 12 6.736 4.533 8.662 0.254
SMC 15 71.352 192.081 643.882 -0.188
SMC 18 20.602 6.741 6.332 2.189
Metro 5 3.764 25.768 50.962 -0.432
Metro 8 10.653 7.363 7.280 0.452
Metro 10 4.093 7.024 9.415 -0.311
Metro 12 6.462 4.533 8.662 0.223
Metro 15 73.306 192.081 643.882 -0.184
Metro 18 22.126 6.741 6.332 2.430
DEMetro_Z 5 4.334 25.768 50.962 -0.421
DEMetro_Z 8 4.353 7.363 7.280 -0.413
DEMetro_Z 10 4.559 7.024 9.415 -0.262
DEMetro_Z 12 5.734 4.533 8.662 0.139
DEMetro_Z 15 75.368 192.081 643.882 -0.181
DEMetro_Z 18 27.696 6.741 6.332 3.309
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 1.369 0.185 0.511
HMC 8 4.510 0.000766 7.581
HMC 10 4.437 0.000852 7.036
HMC 12 3.961 0.00192 5.721
HMC 15 4.058 0.00116 3.304
HMC 18 3.335 0.00652 10.927
SMC 5 4.908 0.00014 3.030
SMC 8 7.911 5.11e-06 13.566
SMC 10 4.777 0.000546 14.653
SMC 12 5.302 0.000165 6.093
SMC 15 4.764 0.000159 2.703
SMC 18 7.002 1.55e-05 10.668
Metro 5 3.714 0.00125 1.660
Metro 8 1.936 0.0788 8.872
Metro 10 4.403 0.000766 4.851
Metro 12 4.840 0.000207 3.420
Metro 15 3.446 0.00263 1.758
Metro 18 2.715 0.0199 10.418
DEMetro_Z 5 4.913 7e-05 1.856
DEMetro_Z 8 5.159 0.000288 13.035
DEMetro_Z 10 5.272 0.000247 15.274
DEMetro_Z 12 4.055 0.00175 8.146
DEMetro_Z 15 3.693 0.0031 5.234
DEMetro_Z 18 4.377 0.00109 26.524
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -0.478 0.642 -0.138
Metro_vs_DEMetro_Z 1 -0.811 0.435 -0.234
Metro_vs_DEMetro_Z 2 -3.452 0.0054 -0.997
Metro_vs_DEMetro_Z 3 -2.409 0.0347 -0.695
Metro_vs_DEMetro_Z 4 -2.696 0.0208 -0.778
Metro_vs_DEMetro_Z 5 -2.118 0.0578 -0.611
DEMetro_Z_vs_SMC 0 -1.924 0.0806 -0.555
DEMetro_Z_vs_SMC 1 -0.171 0.868 -0.049
DEMetro_Z_vs_SMC 2 0.197 0.847 0.057
DEMetro_Z_vs_SMC 3 0.744 0.472 0.215
DEMetro_Z_vs_SMC 4 1.752 0.108 0.506
DEMetro_Z_vs_SMC 5 2.665 0.022 0.769
HMC_vs_DEMetro_Z 0 -4.168 0.00157 -1.203
HMC_vs_DEMetro_Z 1 -1.681 0.121 -0.485
HMC_vs_DEMetro_Z 2 -2.729 0.0196 -0.788
HMC_vs_DEMetro_Z 3 -1.173 0.265 -0.339
HMC_vs_DEMetro_Z 4 -1.297 0.221 -0.374
HMC_vs_DEMetro_Z 5 -1.988 0.0723 -0.574
HMC_vs_Metro 0 -2.526 0.0282 -0.729
HMC_vs_Metro 1 -0.274 0.789 -0.079
HMC_vs_Metro 2 1.080 0.303 0.312
HMC_vs_Metro 3 1.596 0.139 0.461
HMC_vs_Metro 4 2.680 0.0214 0.774
HMC_vs_Metro 5 0.107 0.917 0.031
HMC_vs_SMC 0 -4.528 0.00086 -1.307
HMC_vs_SMC 1 -2.806 0.0171 -0.810
HMC_vs_SMC 2 -2.233 0.0473 -0.645
HMC_vs_SMC 3 -0.174 0.865 -0.050
HMC_vs_SMC 4 0.579 0.574 0.167
HMC_vs_SMC 5 0.069 0.946 0.020
Metro_vs_SMC 0 -2.734 0.0194 -0.789
Metro_vs_SMC 1 -0.844 0.416 -0.244
Metro_vs_SMC 2 -2.779 0.018 -0.802
Metro_vs_SMC 3 -1.747 0.109 -0.504
Metro_vs_SMC 4 -1.512 0.159 -0.436
Metro_vs_SMC 5 -0.059 0.954 -0.017
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.178 0.141 0.074 0.511
HMC 8 0.324 0.136 0.025 7.581
HMC 10 0.358 0.150 0.030 7.036
HMC 12 0.560 0.181 0.066 5.721
HMC 15 0.838 0.224 0.186 3.304
HMC 18 0.875 0.224 0.060 10.927
SMC 5 0.364 0.141 0.074 3.030
SMC 8 0.472 0.136 0.025 13.566
SMC 10 0.584 0.150 0.030 14.653
SMC 12 0.585 0.181 0.066 6.093
SMC 15 0.726 0.224 0.186 2.703
SMC 18 0.859 0.224 0.060 10.668
Metro 5 0.263 0.141 0.074 1.660
Metro 8 0.356 0.136 0.025 8.872
Metro 10 0.293 0.150 0.030 4.851
Metro 12 0.408 0.181 0.066 3.420
Metro 15 0.550 0.224 0.186 1.758
Metro 18 0.845 0.224 0.060 10.418
DEMetro_Z 5 0.277 0.141 0.074 1.856
DEMetro_Z 8 0.459 0.136 0.025 13.035
DEMetro_Z 10 0.602 0.150 0.030 15.274
DEMetro_Z 12 0.721 0.181 0.066 8.146
DEMetro_Z 15 1.196 0.224 0.186 5.234
DEMetro_Z 18 1.804 0.224 0.060 26.524
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 3.163 0.00689 2.594
HMC 8 3.949 0.00212 8.399
HMC 10 4.123 0.00154 7.817
HMC 12 3.652 0.00329 4.889
HMC 15 4.495 0.000885 17.804
HMC 18 3.067 0.0105 10.375
SMC 5 7.755 3.57e-06 8.259
SMC 8 6.343 4.27e-05 10.966
SMC 10 2.866 0.0152 11.220
SMC 12 3.779 0.00215 3.366
SMC 15 4.310 0.00115 10.063
SMC 18 4.277 0.00118 8.166
Metro 5 4.397 0.00057 3.432
Metro 8 3.513 0.00391 3.705
Metro 10 2.964 0.0118 4.046
Metro 12 2.533 0.0224 1.709
Metro 15 4.175 0.00137 7.089
Metro 18 2.615 0.0239 10.580
DEMetro_Z 5 5.826 5.05e-05 5.213
DEMetro_Z 8 4.681 0.00064 14.336
DEMetro_Z 10 4.182 0.0015 16.223
DEMetro_Z 12 3.217 0.00782 6.665
DEMetro_Z 15 3.432 0.00558 28.862
DEMetro_Z 18 3.907 0.00244 30.089
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -2.155 0.0542 -0.622
DEMetro_Z_vs_SMC 1 0.957 0.359 0.276
DEMetro_Z_vs_SMC 2 1.080 0.303 0.312
DEMetro_Z_vs_SMC 3 1.277 0.228 0.369
DEMetro_Z_vs_SMC 4 2.140 0.0556 0.618
DEMetro_Z_vs_SMC 5 2.837 0.0162 0.819
HMC_vs_Metro 0 -0.668 0.518 -0.193
HMC_vs_Metro 1 2.318 0.0407 0.669
HMC_vs_Metro 2 1.515 0.158 0.437
HMC_vs_Metro 3 2.041 0.0659 0.589
HMC_vs_Metro 4 3.280 0.00733 0.947
HMC_vs_Metro 5 -0.041 0.968 -0.012
Metro_vs_DEMetro_Z 0 -1.583 0.142 -0.457
Metro_vs_DEMetro_Z 1 -3.330 0.00671 -0.961
Metro_vs_DEMetro_Z 2 -3.112 0.0099 -0.898
Metro_vs_DEMetro_Z 3 -2.231 0.0475 -0.644
Metro_vs_DEMetro_Z 4 -2.842 0.016 -0.820
Metro_vs_DEMetro_Z 5 -2.157 0.054 -0.623
HMC_vs_SMC 0 -4.182 0.00153 -1.207
HMC_vs_SMC 1 -0.952 0.362 -0.275
HMC_vs_SMC 2 -0.760 0.463 -0.219
HMC_vs_SMC 3 0.868 0.404 0.251
HMC_vs_SMC 4 1.422 0.183 0.410
HMC_vs_SMC 5 0.521 0.612 0.151
Metro_vs_SMC 0 -4.054 0.0019 -1.170
Metro_vs_SMC 1 -3.494 0.00503 -1.009
Metro_vs_SMC 2 -1.644 0.128 -0.475
Metro_vs_SMC 3 -1.387 0.193 -0.400
Metro_vs_SMC 4 -0.921 0.377 -0.266
Metro_vs_SMC 5 0.521 0.612 0.150
HMC_vs_DEMetro_Z 0 -2.096 0.06 -0.605
HMC_vs_DEMetro_Z 1 -1.415 0.185 -0.408
HMC_vs_DEMetro_Z 2 -2.167 0.053 -0.626
HMC_vs_DEMetro_Z 3 -0.838 0.42 -0.242
HMC_vs_DEMetro_Z 4 -1.249 0.237 -0.361
HMC_vs_DEMetro_Z 5 -2.123 0.0573 -0.613
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.025 0.012 0.005 2.594
HMC 8 0.041 0.010 0.004 8.399
HMC 10 0.045 0.011 0.004 7.817
HMC 12 0.064 0.015 0.010 4.889
HMC 15 0.085 0.010 0.004 17.804
HMC 18 0.074 0.013 0.006 10.375
SMC 5 0.054 0.012 0.005 8.259
SMC 8 0.051 0.010 0.004 10.966
SMC 10 0.059 0.011 0.004 11.220
SMC 12 0.049 0.015 0.010 3.366
SMC 15 0.052 0.010 0.004 10.063
SMC 18 0.061 0.013 0.006 8.166
Metro 5 0.029 0.012 0.005 3.432
Metro 8 0.024 0.010 0.004 3.705
Metro 10 0.029 0.011 0.004 4.046
Metro 12 0.033 0.015 0.010 1.709
Metro 15 0.040 0.010 0.004 7.089
Metro 18 0.075 0.013 0.006 10.580
DEMetro_Z 5 0.039 0.012 0.005 5.213
DEMetro_Z 8 0.063 0.010 0.004 14.336
DEMetro_Z 10 0.081 0.011 0.004 16.223
DEMetro_Z 12 0.082 0.015 0.010 6.665
DEMetro_Z 15 0.131 0.010 0.004 28.862
DEMetro_Z 18 0.190 0.013 0.006 30.089
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 2.285 0.0338 1.182
HMC 8 2.859 0.0145 4.200
HMC 10 4.649 0.000528 5.702
HMC 12 2.308 0.039 2.719
HMC 15 2.032 0.0635 2.166
HMC 18 3.520 0.00463 9.205
SMC 5 2.968 0.00939 2.071
SMC 8 4.010 0.00184 6.956
SMC 10 3.543 0.00352 3.368
SMC 12 2.397 0.035 6.554
SMC 15 3.177 0.00774 3.852
SMC 18 3.242 0.00734 5.636
Metro 5 3.735 0.00241 3.501
Metro 8 2.725 0.0194 7.479
Metro 10 3.417 0.00444 3.172
Metro 12 2.106 0.051 1.332
Metro 15 2.690 0.0135 1.187
Metro 18 3.507 0.00472 8.674
DEMetro_Z 5 4.148 0.00113 4.065
DEMetro_Z 8 4.227 0.00114 5.425
DEMetro_Z 10 2.102 0.0583 3.997
DEMetro_Z 12 3.484 0.00386 3.166
DEMetro_Z 15 2.611 0.0236 5.496
DEMetro_Z 18 3.148 0.0092 16.606
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -2.781 0.0179 -0.803
HMC_vs_DEMetro_Z 1 -0.669 0.517 -0.193
HMC_vs_DEMetro_Z 2 0.779 0.452 0.225
HMC_vs_DEMetro_Z 3 -0.280 0.785 -0.081
HMC_vs_DEMetro_Z 4 -1.239 0.241 -0.358
HMC_vs_DEMetro_Z 5 -1.148 0.275 -0.331
Metro_vs_SMC 0 1.150 0.274 0.332
Metro_vs_SMC 1 0.137 0.893 0.040
Metro_vs_SMC 2 -0.121 0.906 -0.035
Metro_vs_SMC 3 -1.785 0.102 -0.515
Metro_vs_SMC 4 -1.978 0.0735 -0.571
Metro_vs_SMC 5 1.176 0.264 0.340
Metro_vs_DEMetro_Z 0 -0.420 0.683 -0.121
Metro_vs_DEMetro_Z 1 0.939 0.368 0.271
Metro_vs_DEMetro_Z 2 -0.343 0.738 -0.099
Metro_vs_DEMetro_Z 3 -1.649 0.127 -0.476
Metro_vs_DEMetro_Z 4 -2.017 0.0687 -0.582
Metro_vs_DEMetro_Z 5 -1.354 0.203 -0.391
HMC_vs_Metro 0 -2.078 0.0619 -0.600
HMC_vs_Metro 1 -1.230 0.244 -0.355
HMC_vs_Metro 2 1.483 0.166 0.428
HMC_vs_Metro 3 1.018 0.33 0.294
HMC_vs_Metro 4 0.831 0.423 0.240
HMC_vs_Metro 5 0.156 0.879 0.045
HMC_vs_SMC 0 -1.150 0.274 -0.332
HMC_vs_SMC 1 -1.158 0.271 -0.334
HMC_vs_SMC 2 1.639 0.129 0.473
HMC_vs_SMC 3 -1.648 0.128 -0.476
HMC_vs_SMC 4 -1.479 0.167 -0.427
HMC_vs_SMC 5 1.069 0.308 0.309
DEMetro_Z_vs_SMC 0 1.818 0.0964 0.525
DEMetro_Z_vs_SMC 1 -0.693 0.503 -0.200
DEMetro_Z_vs_SMC 2 0.440 0.668 0.127
DEMetro_Z_vs_SMC 3 -1.323 0.213 -0.382
DEMetro_Z_vs_SMC 4 0.760 0.463 0.219
DEMetro_Z_vs_SMC 5 2.008 0.0699 0.580
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.089 0.049 0.034 1.182
HMC 8 0.178 0.059 0.028 4.200
HMC 10 0.383 0.098 0.050 5.702
HMC 12 0.381 0.134 0.091 2.719
HMC 15 0.547 0.153 0.182 2.166
HMC 18 0.942 0.168 0.084 9.205
SMC 5 0.119 0.049 0.034 2.071
SMC 8 0.256 0.059 0.028 6.956
SMC 10 0.267 0.098 0.050 3.368
SMC 12 0.729 0.134 0.091 6.554
SMC 15 0.853 0.153 0.182 3.852
SMC 18 0.642 0.168 0.084 5.636
Metro 5 0.168 0.049 0.034 3.501
Metro 8 0.271 0.059 0.028 7.479
Metro 10 0.257 0.098 0.050 3.172
Metro 12 0.255 0.134 0.091 1.332
Metro 15 0.369 0.153 0.182 1.187
Metro 18 0.898 0.168 0.084 8.674
DEMetro_Z 5 0.187 0.049 0.034 4.065
DEMetro_Z 8 0.213 0.059 0.028 5.425
DEMetro_Z 10 0.298 0.098 0.050 3.997
DEMetro_Z 12 0.422 0.134 0.091 3.166
DEMetro_Z 15 1.152 0.153 0.182 5.496
DEMetro_Z 18 1.565 0.168 0.084 16.606
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 -1.584 0.141 -0.458
HMC 8 -0.142 0.888 -0.080
HMC 10 -1.066 0.306 -0.321
HMC 12 -0.272 0.789 -0.083
HMC 15 -0.600 0.558 -0.183
HMC 18 1.000 0.338 2.558
SMC 5 -1.527 0.155 -0.441
SMC 8 -1.698 0.114 -0.507
SMC 10 -1.221 0.242 -0.379
SMC 12 0.321 0.752 0.101
SMC 15 -0.612 0.55 -0.187
SMC 18 0.873 0.401 2.216
Metro 5 -1.505 0.16 -0.435
Metro 8 0.384 0.707 0.353
Metro 10 -1.117 0.284 -0.338
Metro 12 -0.201 0.844 -0.061
Metro 15 -0.598 0.559 -0.183
Metro 18 1.325 0.212 3.475
DEMetro_Z 5 -1.545 0.151 -0.446
DEMetro_Z 8 -1.686 0.113 -0.527
DEMetro_Z 10 -0.853 0.408 -0.264
DEMetro_Z 12 0.069 0.946 0.021
DEMetro_Z 15 -0.601 0.557 -0.184
DEMetro_Z 18 1.184 0.261 3.066
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -1.113 0.289 -0.321
HMC_vs_SMC 1 0.935 0.37 0.270
HMC_vs_SMC 2 0.763 0.462 0.220
HMC_vs_SMC 3 -1.214 0.25 -0.351
HMC_vs_SMC 4 0.951 0.362 0.275
HMC_vs_SMC 5 0.978 0.349 0.282
Metro_vs_DEMetro_Z 0 1.462 0.172 0.422
Metro_vs_DEMetro_Z 1 1.023 0.328 0.295
Metro_vs_DEMetro_Z 2 -1.824 0.0953 -0.527
Metro_vs_DEMetro_Z 3 -1.802 0.0991 -0.520
Metro_vs_DEMetro_Z 4 0.213 0.835 0.062
Metro_vs_DEMetro_Z 5 0.382 0.71 0.110
HMC_vs_Metro 0 -2.117 0.0578 -0.611
HMC_vs_Metro 1 -0.419 0.684 -0.121
HMC_vs_Metro 2 0.267 0.794 0.077
HMC_vs_Metro 3 -0.291 0.777 -0.084
HMC_vs_Metro 4 -0.092 0.929 -0.026
HMC_vs_Metro 5 -0.908 0.383 -0.262
HMC_vs_DEMetro_Z 0 -0.883 0.396 -0.255
HMC_vs_DEMetro_Z 1 0.922 0.376 0.266
HMC_vs_DEMetro_Z 2 -0.741 0.474 -0.214
HMC_vs_DEMetro_Z 3 -1.336 0.208 -0.386
HMC_vs_DEMetro_Z 4 0.097 0.924 0.028
HMC_vs_DEMetro_Z 5 -0.875 0.4 -0.253
Metro_vs_SMC 0 0.420 0.683 0.121
Metro_vs_SMC 1 0.971 0.353 0.280
Metro_vs_SMC 2 0.691 0.504 0.200
Metro_vs_SMC 3 -1.084 0.301 -0.313
Metro_vs_SMC 4 0.881 0.397 0.254
Metro_vs_SMC 5 1.369 0.198 0.395
DEMetro_Z_vs_SMC 0 -0.241 0.814 -0.070
DEMetro_Z_vs_SMC 1 -0.180 0.861 -0.052
DEMetro_Z_vs_SMC 2 1.628 0.132 0.470
DEMetro_Z_vs_SMC 3 -0.482 0.64 -0.139
DEMetro_Z_vs_SMC 4 1.425 0.182 0.411
DEMetro_Z_vs_SMC 5 1.956 0.0764 0.565
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 2.451 25.768 50.962 -0.458
HMC 8 6.781 7.363 7.280 -0.080
HMC 10 3.999 7.024 9.415 -0.321
HMC 12 3.817 4.533 8.662 -0.083
HMC 15 74.092 192.081 643.882 -0.183
HMC 18 22.938 6.741 6.332 2.558
SMC 5 3.271 25.768 50.962 -0.441
SMC 8 3.670 7.363 7.280 -0.507
SMC 10 3.458 7.024 9.415 -0.379
SMC 12 5.408 4.533 8.662 0.101
SMC 15 71.698 192.081 643.882 -0.187
SMC 18 20.773 6.741 6.332 2.216
Metro 5 3.622 25.768 50.962 -0.435
Metro 8 9.933 7.363 7.280 0.353
Metro 10 3.843 7.024 9.415 -0.338
Metro 12 4.003 4.533 8.662 -0.061
Metro 15 74.451 192.081 643.882 -0.183
Metro 18 28.742 6.741 6.332 3.475
DEMetro_Z 5 3.025 25.768 50.962 -0.446
DEMetro_Z 8 3.525 7.363 7.280 -0.527
DEMetro_Z 10 4.542 7.024 9.415 -0.264
DEMetro_Z 12 4.718 4.533 8.662 0.021
DEMetro_Z 15 73.823 192.081 643.882 -0.184
DEMetro_Z 18 26.155 6.741 6.332 3.066
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 0.900 0.38 0.301
HMC 8 3.940 0.00195 5.352
HMC 10 5.575 0.000135 9.459
HMC 12 2.663 0.0209 4.016
HMC 15 2.219 0.0444 2.074
HMC 18 3.877 0.00251 12.927
SMC 5 2.229 0.037 1.042
SMC 8 5.401 0.000181 9.739
SMC 10 5.142 0.000238 6.814
SMC 12 3.180 0.00859 9.923
SMC 15 3.399 0.00481 3.489
SMC 18 4.524 0.000776 8.810
Metro 5 3.229 0.00407 1.522
Metro 8 2.827 0.0162 8.217
Metro 10 5.264 0.000185 6.490
Metro 12 2.920 0.0113 2.464
Metro 15 3.412 0.0025 1.408
Metro 18 3.546 0.00449 12.392
DEMetro_Z 5 4.340 0.000281 1.965
DEMetro_Z 8 5.313 0.000171 6.575
DEMetro_Z 10 3.367 0.00605 8.307
DEMetro_Z 12 5.410 0.000115 5.220
DEMetro_Z 15 2.901 0.0136 4.837
DEMetro_Z 18 3.313 0.00688 21.874
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -0.893 0.391 -0.258
Metro_vs_DEMetro_Z 1 0.767 0.459 0.221
Metro_vs_DEMetro_Z 2 -0.588 0.569 -0.170
Metro_vs_DEMetro_Z 3 -2.132 0.0564 -0.615
Metro_vs_DEMetro_Z 4 -2.089 0.0607 -0.603
Metro_vs_DEMetro_Z 5 -1.277 0.228 -0.369
DEMetro_Z_vs_SMC 0 2.572 0.0259 0.743
DEMetro_Z_vs_SMC 1 -1.186 0.26 -0.342
DEMetro_Z_vs_SMC 2 0.702 0.498 0.203
DEMetro_Z_vs_SMC 3 -1.638 0.13 -0.473
DEMetro_Z_vs_SMC 4 0.814 0.433 0.235
DEMetro_Z_vs_SMC 5 1.937 0.0788 0.559
HMC_vs_DEMetro_Z 0 -3.846 0.00272 -1.110
HMC_vs_DEMetro_Z 1 -0.724 0.484 -0.209
HMC_vs_DEMetro_Z 2 0.375 0.715 0.108
HMC_vs_DEMetro_Z 3 -0.641 0.534 -0.185
HMC_vs_DEMetro_Z 4 -1.283 0.226 -0.370
HMC_vs_DEMetro_Z 5 -1.117 0.288 -0.322
HMC_vs_Metro 0 -2.822 0.0166 -0.815
HMC_vs_Metro 1 -0.995 0.341 -0.287
HMC_vs_Metro 2 1.316 0.215 0.380
HMC_vs_Metro 3 0.828 0.425 0.239
HMC_vs_Metro 4 0.648 0.53 0.187
HMC_vs_Metro 5 0.125 0.903 0.036
HMC_vs_SMC 0 -1.627 0.132 -0.470
HMC_vs_SMC 1 -1.851 0.0912 -0.534
HMC_vs_SMC 2 1.472 0.169 0.425
HMC_vs_SMC 3 -2.188 0.0511 -0.632
HMC_vs_SMC 4 -1.446 0.176 -0.417
HMC_vs_SMC 5 0.960 0.358 0.277
Metro_vs_SMC 0 0.838 0.42 0.242
Metro_vs_SMC 1 -0.367 0.72 -0.106
Metro_vs_SMC 2 -0.140 0.891 -0.041
Metro_vs_SMC 3 -2.196 0.0505 -0.634
Metro_vs_SMC 4 -1.893 0.085 -0.546
Metro_vs_SMC 5 1.068 0.308 0.308
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.163 0.141 0.074 0.301
HMC 8 0.268 0.136 0.025 5.352
HMC 10 0.430 0.150 0.030 9.459
HMC 12 0.447 0.181 0.066 4.016
HMC 15 0.609 0.224 0.186 2.074
HMC 18 0.994 0.224 0.060 12.927
SMC 5 0.217 0.141 0.074 1.042
SMC 8 0.377 0.136 0.025 9.739
SMC 10 0.352 0.150 0.030 6.814
SMC 12 0.839 0.181 0.066 9.923
SMC 15 0.872 0.224 0.186 3.489
SMC 18 0.749 0.224 0.060 8.810
Metro 5 0.253 0.141 0.074 1.522
Metro 8 0.340 0.136 0.025 8.217
Metro 10 0.342 0.150 0.030 6.490
Metro 12 0.344 0.181 0.066 2.464
Metro 15 0.485 0.224 0.186 1.408
Metro 18 0.962 0.224 0.060 12.392
DEMetro_Z 5 0.285 0.141 0.074 1.965
DEMetro_Z 8 0.299 0.136 0.025 6.575
DEMetro_Z 10 0.396 0.150 0.030 8.307
DEMetro_Z 12 0.527 0.181 0.066 5.220
DEMetro_Z 15 1.123 0.224 0.186 4.837
DEMetro_Z 18 1.527 0.224 0.060 21.874
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 2.538 0.0216 1.608
HMC 8 2.922 0.0134 6.220
HMC 10 5.157 0.000276 10.434
HMC 12 2.333 0.0379 3.234
HMC 15 2.303 0.0416 11.079
HMC 18 3.503 0.00486 12.766
SMC 5 3.284 0.00616 3.635
SMC 8 4.494 0.000843 10.379
SMC 10 4.508 0.000756 7.186
SMC 12 2.620 0.0236 8.892
SMC 15 3.096 0.0101 19.432
SMC 18 3.491 0.0048 7.528
Metro 5 3.566 0.00365 4.066
Metro 8 5.728 4.62e-05 4.441
Metro 10 4.230 0.00117 5.869
Metro 12 2.421 0.0291 1.862
Metro 15 3.717 0.00301 5.610
Metro 18 3.631 0.00382 10.171
DEMetro_Z 5 5.470 8.65e-05 4.654
DEMetro_Z 8 3.869 0.00236 6.746
DEMetro_Z 10 2.281 0.0432 7.980
DEMetro_Z 12 4.614 0.000445 4.183
DEMetro_Z 15 2.551 0.0269 27.624
DEMetro_Z 18 3.102 0.01 23.493
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 1.186 0.261 0.342
DEMetro_Z_vs_SMC 1 -1.072 0.307 -0.309
DEMetro_Z_vs_SMC 2 0.287 0.78 0.083
DEMetro_Z_vs_SMC 3 -1.547 0.15 -0.447
DEMetro_Z_vs_SMC 4 0.746 0.472 0.215
DEMetro_Z_vs_SMC 5 2.037 0.0665 0.588
HMC_vs_Metro 0 -1.794 0.1 -0.518
HMC_vs_Metro 1 0.785 0.449 0.227
HMC_vs_Metro 2 1.745 0.109 0.504
HMC_vs_Metro 3 0.792 0.445 0.229
HMC_vs_Metro 4 1.067 0.309 0.308
HMC_vs_Metro 5 0.561 0.586 0.162
Metro_vs_DEMetro_Z 0 -0.395 0.701 -0.114
Metro_vs_DEMetro_Z 1 -1.295 0.222 -0.374
Metro_vs_DEMetro_Z 2 -0.537 0.602 -0.155
Metro_vs_DEMetro_Z 3 -1.887 0.0859 -0.545
Metro_vs_DEMetro_Z 4 -2.009 0.0697 -0.580
Metro_vs_DEMetro_Z 5 -1.638 0.13 -0.473
HMC_vs_SMC 0 -1.477 0.168 -0.426
HMC_vs_SMC 1 -1.219 0.248 -0.352
HMC_vs_SMC 2 1.443 0.177 0.417
HMC_vs_SMC 3 -1.938 0.0787 -0.559
HMC_vs_SMC 4 -1.471 0.169 -0.425
HMC_vs_SMC 5 1.124 0.285 0.325
Metro_vs_SMC 0 0.243 0.812 0.070
Metro_vs_SMC 1 -2.135 0.0561 -0.616
Metro_vs_SMC 2 -0.508 0.621 -0.147
Metro_vs_SMC 3 -1.922 0.0809 -0.555
Metro_vs_SMC 4 -2.147 0.0549 -0.620
Metro_vs_SMC 5 0.895 0.39 0.258
HMC_vs_DEMetro_Z 0 -2.804 0.0171 -0.810
HMC_vs_DEMetro_Z 1 -0.233 0.82 -0.067
HMC_vs_DEMetro_Z 2 0.627 0.543 0.181
HMC_vs_DEMetro_Z 3 -0.564 0.584 -0.163
HMC_vs_DEMetro_Z 4 -1.249 0.238 -0.361
HMC_vs_DEMetro_Z 5 -1.162 0.27 -0.335
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.020 0.012 0.005 1.608
HMC 8 0.033 0.010 0.004 6.220
HMC 10 0.056 0.011 0.004 10.434
HMC 12 0.048 0.015 0.010 3.234
HMC 15 0.057 0.010 0.004 11.079
HMC 18 0.088 0.013 0.006 12.766
SMC 5 0.031 0.012 0.005 3.635
SMC 8 0.048 0.010 0.004 10.379
SMC 10 0.042 0.011 0.004 7.186
SMC 12 0.104 0.015 0.010 8.892
SMC 15 0.092 0.010 0.004 19.432
SMC 18 0.057 0.013 0.006 7.528
Metro 5 0.033 0.012 0.005 4.066
Metro 8 0.027 0.010 0.004 4.441
Metro 10 0.036 0.011 0.004 5.869
Metro 12 0.034 0.015 0.010 1.862
Metro 15 0.034 0.010 0.004 5.610
Metro 18 0.073 0.013 0.006 10.171
DEMetro_Z 5 0.036 0.012 0.005 4.654
DEMetro_Z 8 0.035 0.010 0.004 6.746
DEMetro_Z 10 0.045 0.011 0.004 7.980
DEMetro_Z 12 0.057 0.015 0.010 4.183
DEMetro_Z 15 0.126 0.010 0.004 27.624
DEMetro_Z 18 0.151 0.013 0.006 23.493
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
12 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
18 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
12 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
18 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
5
8
10
12
15
18
Chain
5
8
10
12
15
18

two_attr_tails

▼

Varying_Tails_with_high_Dimension (MvStudentT, nu, 12 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.596 0.137 2.606
HMC 3.0 1.163 0.269 8.747
HMC 4.0 -3.657 0.00157 -1.808
HMC 10.0 -2.044 0.0536 -0.768
HMC 50.0 -3.053 0.00584 -1.276
SMC 2.1 12.489 2.47e-11 4.760
SMC 3.0 24.103 1.96e-11 36.096
SMC 4.0 21.266 2.24e-10 75.162
SMC 10.0 16.618 1.57e-09 26.142
SMC 50.0 6.784 2.41e-06 3.828
Metro 2.1 2.705 0.0203 12.410
Metro 3.0 6.069 6.64e-05 11.462
Metro 4.0 8.807 1.88e-06 16.961
Metro 10.0 12.455 2.04e-10 6.793
Metro 50.0 8.122 3.25e-07 4.984
DEMetro_Z 2.1 19.696 6.22e-10 285.641
DEMetro_Z 3.0 16.588 3.93e-09 554.963
DEMetro_Z 4.0 19.689 6.31e-10 865.188
DEMetro_Z 10.0 11.223 2.3e-07 273.849
DEMetro_Z 50.0 11.533 1.74e-07 215.971
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -18.882 9.9e-10 -5.451
HMC_vs_DEMetro_Z 1 -15.928 6.05e-09 -4.598
HMC_vs_DEMetro_Z 2 -19.801 5.95e-10 -5.716
HMC_vs_DEMetro_Z 3 -11.288 2.18e-07 -3.259
HMC_vs_DEMetro_Z 4 -11.618 1.62e-07 -3.354
Metro_vs_SMC 0 1.642 0.129 0.474
Metro_vs_SMC 1 -11.956 1.21e-07 -3.452
Metro_vs_SMC 2 -13.048 4.9e-08 -3.767
Metro_vs_SMC 3 -14.707 1.4e-08 -4.246
Metro_vs_SMC 4 1.552 0.149 0.448
Metro_vs_DEMetro_Z 0 -17.250 2.6e-09 -4.980
Metro_vs_DEMetro_Z 1 -16.354 4.57e-09 -4.721
Metro_vs_DEMetro_Z 2 -19.137 8.58e-10 -5.524
Metro_vs_DEMetro_Z 3 -10.884 3.15e-07 -3.142
Metro_vs_DEMetro_Z 4 -11.383 2e-07 -3.286
HMC_vs_Metro 0 -1.928 0.08 -0.557
HMC_vs_Metro 1 -0.330 0.748 -0.095
HMC_vs_Metro 2 -10.010 7.32e-07 -2.890
HMC_vs_Metro 3 -14.919 1.21e-08 -4.307
HMC_vs_Metro 4 -11.401 1.97e-07 -3.291
HMC_vs_SMC 0 -1.423 0.183 -0.411
HMC_vs_SMC 1 -3.525 0.00476 -1.018
HMC_vs_SMC 2 -21.295 2.72e-10 -6.147
HMC_vs_SMC 3 -16.703 3.66e-09 -4.822
HMC_vs_SMC 4 -8.596 3.28e-06 -2.481
DEMetro_Z_vs_SMC 0 19.344 7.64e-10 5.584
DEMetro_Z_vs_SMC 1 15.411 8.57e-09 4.449
DEMetro_Z_vs_SMC 2 17.963 1.69e-09 5.186
DEMetro_Z_vs_SMC 3 9.903 8.15e-07 2.859
DEMetro_Z_vs_SMC 4 11.248 2.26e-07 3.247
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.140 0.071 0.027 2.606
HMC 3.0 0.074 0.037 0.004 8.747
HMC 4.0 0.028 0.031 0.002 -1.808
HMC 10.0 0.023 0.025 0.003 -0.768
HMC 50.0 0.019 0.023 0.003 -1.276
SMC 2.1 0.197 0.071 0.027 4.760
SMC 3.0 0.190 0.037 0.004 36.096
SMC 4.0 0.182 0.031 0.002 75.162
SMC 10.0 0.112 0.025 0.003 26.142
SMC 50.0 0.035 0.023 0.003 3.828
Metro 2.1 0.401 0.071 0.027 12.410
Metro 3.0 0.085 0.037 0.004 11.462
Metro 4.0 0.065 0.031 0.002 16.961
Metro 10.0 0.048 0.025 0.003 6.793
Metro 50.0 0.039 0.023 0.003 4.984
DEMetro_Z 2.1 7.658 0.071 0.027 285.641
DEMetro_Z 3.0 2.389 0.037 0.004 554.963
DEMetro_Z 4.0 1.768 0.031 0.002 865.188
DEMetro_Z 10.0 0.929 0.025 0.003 273.849
DEMetro_Z 50.0 0.733 0.023 0.003 215.971
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -0.589 0.566 -0.176
HMC 3.0 1.099 0.295 34.663
HMC 4.0 4.162 0.00134 5.973
HMC 10.0 4.735 0.000185 2.806
HMC 50.0 4.446 0.000225 1.641
SMC 2.1 12.941 3.8e-09 3.980
SMC 3.0 37.485 5.74e-13 457.548
SMC 4.0 52.469 1.48e-14 2331.730
SMC 10.0 64.829 1.46e-15 3486.390
SMC 50.0 41.433 1.52e-13 158.562
Metro 2.1 1.119 0.286 2.940
Metro 3.0 2.988 0.00972 2.433
Metro 4.0 3.452 0.00507 6.602
Metro 10.0 7.368 5.31e-06 7.250
Metro 50.0 9.811 3.04e-08 6.272
DEMetro_Z 2.1 10.611 3.52e-07 33.717
DEMetro_Z 3.0 10.177 6.2e-07 383.965
DEMetro_Z 4.0 10.034 7.15e-07 1207.930
DEMetro_Z 10.0 6.239 6.36e-05 1215.821
DEMetro_Z 50.0 5.736 0.000131 1190.490
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -27.841 1.5e-11 -8.037
HMC_vs_SMC 1 -12.133 1.04e-07 -3.503
HMC_vs_SMC 2 -51.865 1.68e-14 -14.972
HMC_vs_SMC 3 -64.675 1.5e-15 -18.670
HMC_vs_SMC 4 -39.410 3.4e-13 -11.377
Metro_vs_DEMetro_Z 0 -6.819 2.88e-05 -1.968
Metro_vs_DEMetro_Z 1 -10.149 6.38e-07 -2.930
Metro_vs_DEMetro_Z 2 -9.935 7.89e-07 -2.868
Metro_vs_DEMetro_Z 3 -6.203 6.69e-05 -1.791
Metro_vs_DEMetro_Z 4 -5.699 0.000138 -1.645
HMC_vs_Metro 0 -1.187 0.26 -0.343
HMC_vs_Metro 1 1.020 0.33 0.294
HMC_vs_Metro 2 -0.223 0.827 -0.064
HMC_vs_Metro 3 -4.747 0.000603 -1.370
HMC_vs_Metro 4 -7.156 1.86e-05 -2.066
HMC_vs_DEMetro_Z 0 -10.752 3.56e-07 -3.104
HMC_vs_DEMetro_Z 1 -7.577 1.09e-05 -2.187
HMC_vs_DEMetro_Z 2 -10.006 7.35e-07 -2.888
HMC_vs_DEMetro_Z 3 -6.231 6.43e-05 -1.799
HMC_vs_DEMetro_Z 4 -5.728 0.000133 -1.653
Metro_vs_SMC 0 -0.404 0.694 -0.117
Metro_vs_SMC 1 -36.713 7.38e-13 -10.598
Metro_vs_SMC 2 -51.531 1.81e-14 -14.876
Metro_vs_SMC 3 -63.934 1.7e-15 -18.456
Metro_vs_SMC 4 -42.086 1.66e-13 -12.149
DEMetro_Z_vs_SMC 0 9.220 1.65e-06 2.662
DEMetro_Z_vs_SMC 1 -1.871 0.0881 -0.540
DEMetro_Z_vs_SMC 2 -7.912 7.26e-06 -2.284
DEMetro_Z_vs_SMC 3 -10.810 3.38e-07 -3.121
DEMetro_Z_vs_SMC 4 4.955 0.000432 1.431
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 5.622 9.632 22.759 -0.176
HMC 3.0 7.576 0.506 0.204 34.663
HMC 4.0 0.350 0.142 0.035 5.973
HMC 10.0 0.072 0.046 0.009 2.806
HMC 50.0 0.045 0.037 0.005 1.641
SMC 2.1 100.204 9.632 22.759 3.980
SMC 3.0 93.825 0.506 0.204 457.548
SMC 4.0 81.195 0.142 0.035 2331.730
SMC 10.0 31.896 0.046 0.009 3486.390
SMC 50.0 0.799 0.037 0.005 158.562
Metro 2.1 76.540 9.632 22.759 2.940
Metro 3.0 1.003 0.506 0.204 2.433
Metro 4.0 0.371 0.142 0.035 6.602
Metro 10.0 0.112 0.046 0.009 7.250
Metro 50.0 0.067 0.037 0.005 6.272
DEMetro_Z 2.1 776.986 9.632 22.759 33.717
DEMetro_Z 3.0 78.818 0.506 0.204 383.965
DEMetro_Z 4.0 42.131 0.142 0.035 1207.930
DEMetro_Z 10.0 11.153 0.046 0.009 1215.821
DEMetro_Z 50.0 5.760 0.037 0.005 1190.490
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 4.641 0.000609 7.654
HMC 3.0 1.423 0.182 100.007
HMC 4.0 3.763 0.00297 8.658
HMC 10.0 2.099 0.0541 1.685
HMC 50.0 -0.672 0.509 -0.304
SMC 2.1 72.581 2.55e-16 225.703
SMC 3.0 60.175 3.29e-15 1927.101
SMC 4.0 87.397 5.47e-17 3137.282
SMC 10.0 108.645 4.97e-18 2506.727
SMC 50.0 43.163 8.88e-14 144.275
Metro 2.1 2.491 0.03 54.418
Metro 3.0 4.892 0.000472 32.666
Metro 4.0 8.499 3.24e-06 25.871
Metro 10.0 15.488 8.91e-10 15.285
Metro 50.0 11.131 8.12e-09 7.604
DEMetro_Z 2.1 23.824 8.09e-11 664.602
DEMetro_Z 3.0 20.244 4.69e-10 1689.311
DEMetro_Z 4.0 20.014 5.3e-10 2049.604
DEMetro_Z 10.0 15.369 8.82e-09 1182.294
DEMetro_Z 50.0 9.875 8.38e-07 614.762
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -15.727 6.92e-09 -4.540
Metro_vs_DEMetro_Z 1 -20.207 4.79e-10 -5.833
Metro_vs_DEMetro_Z 2 -19.740 6.15e-10 -5.699
Metro_vs_DEMetro_Z 3 -15.111 1.05e-08 -4.362
Metro_vs_DEMetro_Z 4 -9.760 9.42e-07 -2.818
DEMetro_Z_vs_SMC 0 14.890 1.23e-08 4.298
DEMetro_Z_vs_SMC 1 -2.663 0.0221 -0.769
DEMetro_Z_vs_SMC 2 -9.151 1.78e-06 -2.642
DEMetro_Z_vs_SMC 3 -15.952 5.95e-09 -4.605
DEMetro_Z_vs_SMC 4 7.494 1.21e-05 2.163
HMC_vs_DEMetro_Z 0 -23.459 9.6e-11 -6.772
HMC_vs_DEMetro_Z 1 -14.721 1.39e-08 -4.250
HMC_vs_DEMetro_Z 2 -20.041 5.23e-10 -5.785
HMC_vs_DEMetro_Z 3 -15.396 8.66e-09 -4.444
HMC_vs_DEMetro_Z 4 -9.891 8.25e-07 -2.855
HMC_vs_Metro 0 -2.084 0.0612 -0.602
HMC_vs_Metro 1 0.929 0.373 0.268
HMC_vs_Metro 2 -3.775 0.00307 -1.090
HMC_vs_Metro 3 -10.809 3.38e-07 -3.120
HMC_vs_Metro 4 -13.647 3.07e-08 -3.940
HMC_vs_SMC 0 -64.343 1.58e-15 -18.574
HMC_vs_SMC 1 -23.727 8.48e-11 -6.850
HMC_vs_SMC 2 -85.284 7.18e-17 -24.619
HMC_vs_SMC 3 -108.641 5.02e-18 -31.362
HMC_vs_SMC 4 -43.798 1.07e-13 -12.643
Metro_vs_SMC 0 -8.107 5.75e-06 -2.340
Metro_vs_SMC 1 -58.857 4.21e-15 -16.990
Metro_vs_SMC 2 -84.395 8.06e-17 -24.363
Metro_vs_SMC 3 -107.662 5.55e-18 -31.079
Metro_vs_SMC 4 -40.155 2.77e-13 -11.592
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.340 0.113 0.030 7.654
HMC 3.0 0.401 0.063 0.003 100.007
HMC 4.0 0.065 0.048 0.002 8.658
HMC 10.0 0.037 0.035 0.001 1.685
HMC 50.0 0.029 0.030 0.002 -0.304
SMC 2.1 6.811 0.113 0.030 225.703
SMC 3.0 6.565 0.063 0.003 1927.101
SMC 4.0 6.120 0.048 0.002 3137.282
SMC 10.0 3.698 0.035 0.001 2506.727
SMC 50.0 0.275 0.030 0.002 144.275
Metro 2.1 1.728 0.113 0.030 54.418
Metro 3.0 0.173 0.063 0.003 32.666
Metro 4.0 0.098 0.048 0.002 25.871
Metro 10.0 0.057 0.035 0.001 15.285
Metro 50.0 0.043 0.030 0.002 7.604
DEMetro_Z 2.1 19.835 0.113 0.030 664.602
DEMetro_Z 3.0 5.763 0.063 0.003 1689.311
DEMetro_Z 4.0 4.015 0.048 0.002 2049.604
DEMetro_Z 10.0 1.762 0.035 0.001 1182.294
DEMetro_Z 50.0 1.075 0.030 0.002 614.762
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 3.983 0.00215 70.392
HMC 3.0 2.461 0.0316 31.981
HMC 4.0 3.252 0.00724 5.841
HMC 10.0 1.240 0.233 0.845
HMC 50.0 -1.265 0.219 -0.517
SMC 2.1 131.350 3.01e-19 375.972
SMC 3.0 70.579 4.28e-16 285.193
SMC 4.0 129.077 4.25e-19 414.167
SMC 10.0 77.545 1.46e-16 298.316
SMC 50.0 42.827 2.1e-14 62.321
Metro 2.1 7.324 1.49e-05 169.487
Metro 3.0 5.270 0.000259 28.240
Metro 4.0 9.447 1.07e-06 23.957
Metro 10.0 14.379 4.01e-10 10.599
Metro 50.0 10.349 7e-09 6.019
DEMetro_Z 2.1 55.783 7.12e-15 462.986
DEMetro_Z 3.0 65.115 1.16e-15 329.625
DEMetro_Z 4.0 51.789 1.63e-14 479.572
DEMetro_Z 10.0 35.821 9.21e-13 310.084
DEMetro_Z 50.0 18.029 1.6e-09 214.204
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 9.696 1.01e-06 2.799
DEMetro_Z_vs_SMC 1 6.990 2.3e-05 2.018
DEMetro_Z_vs_SMC 2 6.388 5.16e-05 1.844
DEMetro_Z_vs_SMC 3 1.283 0.226 0.371
DEMetro_Z_vs_SMC 4 12.391 8.36e-08 3.577
HMC_vs_Metro 0 -3.349 0.00649 -0.967
HMC_vs_Metro 1 0.244 0.811 0.071
HMC_vs_Metro 2 -5.243 0.000276 -1.513
HMC_vs_Metro 3 -10.140 6.43e-07 -2.927
HMC_vs_Metro 4 -11.957 1.21e-07 -3.452
Metro_vs_DEMetro_Z 0 -11.886 1.28e-07 -3.431
Metro_vs_DEMetro_Z 1 -58.457 4.54e-15 -16.875
Metro_vs_DEMetro_Z 2 -50.273 2.37e-14 -14.513
Metro_vs_DEMetro_Z 3 -35.076 1.21e-12 -10.126
Metro_vs_DEMetro_Z 4 -17.648 2.04e-09 -5.095
HMC_vs_SMC 0 -15.694 7.07e-09 -4.531
HMC_vs_SMC 1 -23.151 1.11e-10 -6.683
HMC_vs_SMC 2 -105.119 7.22e-18 -30.345
HMC_vs_SMC 3 -75.862 2.6e-16 -21.899
HMC_vs_SMC 4 -44.714 8.55e-14 -12.908
Metro_vs_SMC 0 -8.609 3.23e-06 -2.485
Metro_vs_SMC 1 -39.162 3.65e-13 -11.305
Metro_vs_SMC 2 -96.209 1.91e-17 -27.773
Metro_vs_SMC 3 -77.592 2.03e-16 -22.399
Metro_vs_SMC 4 -37.335 6.14e-13 -10.778
HMC_vs_DEMetro_Z 0 -20.535 4.03e-10 -5.928
HMC_vs_DEMetro_Z 1 -19.718 6.22e-10 -5.692
HMC_vs_DEMetro_Z 2 -49.684 2.7e-14 -14.343
HMC_vs_DEMetro_Z 3 -35.790 9.74e-13 -10.332
HMC_vs_DEMetro_Z 4 -18.126 1.53e-09 -5.232
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.085 0.015 0.001 70.392
HMC 3.0 0.059 0.015 0.001 31.981
HMC 4.0 0.020 0.014 0.001 5.841
HMC 10.0 0.016 0.015 0.001 0.845
HMC 50.0 0.013 0.014 0.002 -0.517
SMC 2.1 0.390 0.015 0.001 375.972
SMC 3.0 0.402 0.015 0.001 285.193
SMC 4.0 0.401 0.014 0.001 414.167
SMC 10.0 0.382 0.015 0.001 298.316
SMC 50.0 0.114 0.014 0.002 62.321
Metro 2.1 0.184 0.015 0.001 169.487
Metro 3.0 0.054 0.015 0.001 28.240
Metro 4.0 0.037 0.014 0.001 23.957
Metro 10.0 0.028 0.015 0.001 10.599
Metro 50.0 0.024 0.014 0.002 6.019
DEMetro_Z 2.1 0.476 0.015 0.001 462.986
DEMetro_Z 3.0 0.463 0.015 0.001 329.625
DEMetro_Z 4.0 0.463 0.014 0.001 479.572
DEMetro_Z 10.0 0.396 0.015 0.001 310.084
DEMetro_Z 50.0 0.356 0.014 0.002 214.204
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.208 0.252 22.271
HMC 3.0 0.131 0.897 0.075
HMC 4.0 -2.697 0.0138 -1.320
HMC 10.0 -2.420 0.0242 -0.987
HMC 50.0 -3.461 0.00296 -1.140
SMC 2.1 15.137 9.92e-13 7.048
SMC 3.0 16.690 2.11e-09 33.317
SMC 4.0 25.255 3.17e-11 77.619
SMC 10.0 25.943 1.36e-12 25.754
SMC 50.0 5.539 2.93e-05 3.108
Metro 2.1 4.219 0.00114 5.262
Metro 3.0 5.148 0.000289 11.958
Metro 4.0 10.266 3.24e-07 16.322
Metro 10.0 10.252 6.16e-08 8.272
Metro 50.0 12.836 1.74e-11 5.806
DEMetro_Z 2.1 11.427 1.91e-07 276.091
DEMetro_Z 3.0 10.803 3.4e-07 482.510
DEMetro_Z 4.0 18.831 1.02e-09 839.502
DEMetro_Z 10.0 10.606 4.09e-07 273.330
DEMetro_Z 50.0 12.285 9.07e-08 186.415
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -7.651 9.96e-06 -2.209
HMC_vs_DEMetro_Z 1 -10.840 3.28e-07 -3.129
HMC_vs_DEMetro_Z 2 -18.896 9.82e-10 -5.455
HMC_vs_DEMetro_Z 3 -10.649 3.93e-07 -3.074
HMC_vs_DEMetro_Z 4 -12.428 8.11e-08 -3.588
Metro_vs_SMC 0 -1.328 0.211 -0.383
Metro_vs_SMC 1 -8.608 3.24e-06 -2.485
Metro_vs_SMC 2 -21.599 2.34e-10 -6.235
Metro_vs_SMC 3 -13.124 4.61e-08 -3.788
Metro_vs_SMC 4 4.648 0.000707 1.342
Metro_vs_DEMetro_Z 0 -11.082 2.63e-07 -3.199
Metro_vs_DEMetro_Z 1 -10.542 4.35e-07 -3.043
Metro_vs_DEMetro_Z 2 -18.276 1.4e-09 -5.276
Metro_vs_DEMetro_Z 3 -10.323 5.38e-07 -2.980
Metro_vs_DEMetro_Z 4 -11.984 1.18e-07 -3.460
HMC_vs_Metro 0 0.931 0.372 0.269
HMC_vs_Metro 1 -5.082 0.000354 -1.467
HMC_vs_Metro 2 -11.026 2.76e-07 -3.183
HMC_vs_Metro 3 -10.655 3.91e-07 -3.076
HMC_vs_Metro 4 -18.911 9.74e-10 -5.459
HMC_vs_SMC 0 0.828 0.425 0.239
HMC_vs_SMC 1 -15.562 7.73e-09 -4.492
HMC_vs_SMC 2 -24.974 4.88e-11 -7.209
HMC_vs_SMC 3 -31.715 3.64e-12 -9.155
HMC_vs_SMC 4 -10.293 5.54e-07 -2.971
DEMetro_Z_vs_SMC 0 11.165 2.43e-07 3.223
DEMetro_Z_vs_SMC 1 10.230 5.88e-07 2.953
DEMetro_Z_vs_SMC 2 17.138 2.78e-09 4.947
DEMetro_Z_vs_SMC 3 9.782 9.21e-07 2.824
DEMetro_Z_vs_SMC 4 12.149 1.02e-07 3.507
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.663 0.071 0.027 22.271
HMC 3.0 0.037 0.037 0.004 0.075
HMC 4.0 0.029 0.031 0.002 -1.320
HMC 10.0 0.022 0.025 0.003 -0.987
HMC 50.0 0.019 0.023 0.003 -1.140
SMC 2.1 0.258 0.071 0.027 7.048
SMC 3.0 0.178 0.037 0.004 33.317
SMC 4.0 0.187 0.031 0.002 77.619
SMC 10.0 0.110 0.025 0.003 25.754
SMC 50.0 0.033 0.023 0.003 3.108
Metro 2.1 0.211 0.071 0.027 5.262
Metro 3.0 0.087 0.037 0.004 11.958
Metro 4.0 0.064 0.031 0.002 16.322
Metro 10.0 0.053 0.025 0.003 8.272
Metro 50.0 0.042 0.023 0.003 5.806
DEMetro_Z 2.1 7.404 0.071 0.027 276.091
DEMetro_Z 3.0 2.082 0.037 0.004 482.510
DEMetro_Z 4.0 1.717 0.031 0.002 839.502
DEMetro_Z 10.0 0.928 0.025 0.003 273.330
DEMetro_Z 50.0 0.635 0.023 0.003 186.415
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.086 0.293 0.704
HMC 3.0 1.825 0.0842 0.992
HMC 4.0 3.098 0.00811 2.749
HMC 10.0 3.810 0.00137 2.261
HMC 50.0 4.175 0.000418 1.889
SMC 2.1 14.493 1.93e-09 4.380
SMC 3.0 28.146 1.32e-11 421.706
SMC 4.0 34.168 1.62e-12 2268.486
SMC 10.0 33.488 2.01e-12 3164.149
SMC 50.0 14.982 1.12e-08 115.994
Metro 2.1 0.081 0.936 0.025
Metro 3.0 1.809 0.0962 2.982
Metro 4.0 7.255 1.21e-05 12.711
Metro 10.0 9.537 1.11e-07 7.171
Metro 50.0 14.230 4.42e-12 6.816
DEMetro_Z 2.1 6.746 2.8e-05 17.221
DEMetro_Z 3.0 5.812 0.000117 152.676
DEMetro_Z 4.0 9.772 9.3e-07 572.254
DEMetro_Z 10.0 4.697 0.000654 399.180
DEMetro_Z 50.0 4.179 0.00154 421.943
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -5.761 0.000126 -1.663
HMC_vs_SMC 1 -28.049 1.38e-11 -8.097
HMC_vs_SMC 2 -34.301 1.55e-12 -9.902
HMC_vs_SMC 3 -33.476 2.02e-12 -9.664
HMC_vs_SMC 4 -14.716 1.39e-08 -4.248
Metro_vs_DEMetro_Z 0 -6.692 3.41e-05 -1.932
Metro_vs_DEMetro_Z 1 -5.751 0.000128 -1.660
Metro_vs_DEMetro_Z 2 -9.476 1.26e-06 -2.735
Metro_vs_DEMetro_Z 3 -4.626 0.000733 -1.335
Metro_vs_DEMetro_Z 4 -4.111 0.00173 -1.187
HMC_vs_Metro 0 1.179 0.263 0.340
HMC_vs_Metro 1 -1.326 0.212 -0.383
HMC_vs_Metro 2 -4.852 0.000509 -1.401
HMC_vs_Metro 3 -6.592 3.91e-05 -1.903
HMC_vs_Metro 4 -9.611 1.1e-06 -2.774
HMC_vs_DEMetro_Z 0 -6.016 8.73e-05 -1.737
HMC_vs_DEMetro_Z 1 -5.780 0.000123 -1.668
HMC_vs_DEMetro_Z 2 -9.775 9.27e-07 -2.822
HMC_vs_DEMetro_Z 3 -4.671 0.000681 -1.348
HMC_vs_DEMetro_Z 4 -4.163 0.00158 -1.202
Metro_vs_SMC 0 -26.425 2.65e-11 -7.628
Metro_vs_SMC 1 -26.598 2.46e-11 -7.678
Metro_vs_SMC 2 -33.555 1.97e-12 -9.687
Metro_vs_SMC 3 -33.385 2.08e-12 -9.638
Metro_vs_SMC 4 -14.072 2.23e-08 -4.062
DEMetro_Z_vs_SMC 0 5.112 0.000338 1.476
DEMetro_Z_vs_SMC 1 -8.040 6.23e-06 -2.321
DEMetro_Z_vs_SMC 2 -22.709 1.36e-10 -6.555
DEMetro_Z_vs_SMC 3 -26.997 2.1e-11 -7.793
DEMetro_Z_vs_SMC 4 3.076 0.0105 0.888
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 25.661 9.632 22.759 0.704
HMC 3.0 0.709 0.506 0.204 0.992
HMC 4.0 0.238 0.142 0.035 2.749
HMC 10.0 0.067 0.046 0.009 2.261
HMC 50.0 0.046 0.037 0.005 1.889
SMC 2.1 109.311 9.632 22.759 4.380
SMC 3.0 86.515 0.506 0.204 421.706
SMC 4.0 78.996 0.142 0.035 2268.486
SMC 10.0 28.952 0.046 0.009 3164.149
SMC 50.0 0.594 0.037 0.005 115.994
Metro 2.1 10.198 9.632 22.759 0.025
Metro 3.0 1.114 0.506 0.204 2.982
Metro 4.0 0.584 0.142 0.035 12.711
Metro 10.0 0.112 0.046 0.009 7.171
Metro 50.0 0.069 0.037 0.005 6.816
DEMetro_Z 2.1 401.563 9.632 22.759 17.221
DEMetro_Z 3.0 31.645 0.506 0.204 152.676
DEMetro_Z 4.0 20.034 0.142 0.035 572.254
DEMetro_Z 10.0 3.693 0.046 0.009 399.180
DEMetro_Z 50.0 2.065 0.037 0.005 421.943
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.006 0.07 51.682
HMC 3.0 3.487 0.00475 6.609
HMC 4.0 2.958 0.0127 7.318
HMC 10.0 1.304 0.211 0.847
HMC 50.0 0.076 0.94 0.026
SMC 2.1 107.341 1.76e-18 233.885
SMC 3.0 46.063 6.16e-14 1810.192
SMC 4.0 57.894 5.04e-15 3054.026
SMC 10.0 53.263 1.26e-14 2366.197
SMC 50.0 15.484 7.81e-09 108.270
Metro 2.1 3.722 0.00332 17.083
Metro 3.0 2.523 0.0283 38.224
Metro 4.0 10.613 3.65e-07 38.890
Metro 10.0 11.407 1.01e-07 17.693
Metro 50.0 13.536 2.88e-10 8.685
DEMetro_Z 2.1 14.001 2.35e-08 487.328
DEMetro_Z 3.0 9.161 1.76e-06 988.796
DEMetro_Z 4.0 16.760 3.53e-09 1377.139
DEMetro_Z 10.0 10.034 7.15e-07 699.782
DEMetro_Z 50.0 11.030 2.75e-07 363.622
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -13.077 4.79e-08 -3.775
Metro_vs_DEMetro_Z 1 -8.756 2.74e-06 -2.528
Metro_vs_DEMetro_Z 2 -16.187 5.1e-09 -4.673
Metro_vs_DEMetro_Z 3 -9.860 8.51e-07 -2.846
Metro_vs_DEMetro_Z 4 -10.811 3.37e-07 -3.121
DEMetro_Z_vs_SMC 0 7.302 1.54e-05 2.108
DEMetro_Z_vs_SMC 1 -6.646 3.63e-05 -1.919
DEMetro_Z_vs_SMC 2 -21.212 2.84e-10 -6.123
DEMetro_Z_vs_SMC 3 -22.180 1.76e-10 -6.403
DEMetro_Z_vs_SMC 4 8.180 5.28e-06 2.361
HMC_vs_DEMetro_Z 0 -8.803 2.6e-06 -2.541
HMC_vs_DEMetro_Z 1 -9.153 1.78e-06 -2.642
HMC_vs_DEMetro_Z 2 -16.771 3.5e-09 -4.841
HMC_vs_DEMetro_Z 3 -10.020 7.25e-07 -2.892
HMC_vs_DEMetro_Z 4 -11.060 2.68e-07 -3.193
HMC_vs_Metro 0 1.340 0.207 0.387
HMC_vs_Metro 1 -2.054 0.0645 -0.593
HMC_vs_Metro 2 -6.483 4.53e-05 -1.871
HMC_vs_Metro 3 -9.872 8.4e-07 -2.850
HMC_vs_Metro 4 -16.207 5.03e-09 -4.679
HMC_vs_SMC 0 -6.786 3.01e-05 -1.959
HMC_vs_SMC 1 -46.428 5.67e-14 -13.403
HMC_vs_SMC 2 -59.329 3.86e-15 -17.127
HMC_vs_SMC 3 -53.452 1.21e-14 -15.430
HMC_vs_SMC 4 -15.571 7.68e-09 -4.495
Metro_vs_SMC 0 -42.411 1.53e-13 -12.243
Metro_vs_SMC 1 -36.795 7.2e-13 -10.622
Metro_vs_SMC 2 -55.708 7.69e-15 -16.082
Metro_vs_SMC 3 -52.752 1.4e-14 -15.228
Metro_vs_SMC 4 -14.214 2.01e-08 -4.103
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 1.647 0.113 0.030 51.682
HMC 3.0 0.085 0.063 0.003 6.609
HMC 4.0 0.062 0.048 0.002 7.318
HMC 10.0 0.036 0.035 0.001 0.847
HMC 50.0 0.030 0.030 0.002 0.026
SMC 2.1 7.054 0.113 0.030 233.885
SMC 3.0 6.171 0.063 0.003 1810.192
SMC 4.0 5.959 0.048 0.002 3054.026
SMC 10.0 3.492 0.035 0.001 2366.197
SMC 50.0 0.214 0.030 0.002 108.270
Metro 2.1 0.620 0.113 0.030 17.083
Metro 3.0 0.192 0.063 0.003 38.224
Metro 4.0 0.123 0.048 0.002 38.890
Metro 10.0 0.060 0.035 0.001 17.693
Metro 50.0 0.045 0.030 0.002 8.685
DEMetro_Z 2.1 14.575 0.113 0.030 487.328
DEMetro_Z 3.0 3.399 0.063 0.003 988.796
DEMetro_Z 4.0 2.713 0.048 0.002 1377.139
DEMetro_Z 10.0 1.057 0.035 0.001 699.782
DEMetro_Z 50.0 0.648 0.030 0.002 363.622
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.999 0.0709 158.396
HMC 3.0 2.093 0.0591 3.693
HMC 4.0 2.605 0.0238 5.598
HMC 10.0 0.470 0.644 0.278
HMC 50.0 -1.058 0.305 -0.345
SMC 2.1 68.670 6.7e-16 390.953
SMC 3.0 107.307 2.76e-18 295.980
SMC 4.0 80.205 1.19e-16 435.426
SMC 10.0 140.891 7.39e-20 298.961
SMC 50.0 17.790 1.36e-09 47.903
Metro 2.1 5.030 0.000384 82.876
Metro 3.0 3.353 0.00643 30.151
Metro 4.0 9.890 7.33e-07 33.265
Metro 10.0 13.640 2.86e-09 12.314
Metro 50.0 15.170 4.48e-13 6.486
DEMetro_Z 2.1 27.731 1.55e-11 512.316
DEMetro_Z 3.0 25.640 3.6e-11 331.008
DEMetro_Z 4.0 46.360 5.55e-14 479.131
DEMetro_Z 10.0 16.548 4.01e-09 297.622
DEMetro_Z 50.0 25.866 3.12e-11 170.418
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 6.042 8.4e-05 1.744
DEMetro_Z_vs_SMC 1 2.532 0.0279 0.731
DEMetro_Z_vs_SMC 2 3.138 0.00945 0.906
DEMetro_Z_vs_SMC 3 -0.075 0.941 -0.022
DEMetro_Z_vs_SMC 4 20.347 4.44e-10 5.874
HMC_vs_Metro 0 1.026 0.327 0.296
HMC_vs_Metro 1 -2.742 0.0192 -0.792
HMC_vs_Metro 2 -7.082 2.04e-05 -2.045
HMC_vs_Metro 3 -11.791 1.39e-07 -3.404
HMC_vs_Metro 4 -21.887 2.03e-10 -6.318
Metro_vs_DEMetro_Z 0 -20.439 4.23e-10 -5.900
Metro_vs_DEMetro_Z 1 -27.606 1.65e-11 -7.969
Metro_vs_DEMetro_Z 2 -38.174 4.82e-13 -11.020
Metro_vs_DEMetro_Z 3 -16.147 5.24e-09 -4.661
Metro_vs_DEMetro_Z 4 -25.561 3.79e-11 -7.379
HMC_vs_SMC 0 -2.939 0.0135 -0.849
HMC_vs_SMC 1 -97.171 1.71e-17 -28.051
HMC_vs_SMC 2 -78.286 1.84e-16 -22.599
HMC_vs_SMC 3 -133.505 5.21e-19 -38.539
HMC_vs_SMC 4 -18.248 1.43e-09 -5.268
Metro_vs_SMC 0 -15.954 5.95e-09 -4.605
Metro_vs_SMC 1 -28.184 1.31e-11 -8.136
Metro_vs_SMC 2 -67.339 9.61e-16 -19.439
Metro_vs_SMC 3 -127.001 9.03e-19 -36.662
Metro_vs_SMC 4 -15.103 1.06e-08 -4.360
HMC_vs_DEMetro_Z 0 -4.040 0.00195 -1.166
HMC_vs_DEMetro_Z 1 -25.610 3.71e-11 -7.393
HMC_vs_DEMetro_Z 2 -48.257 3.71e-14 -13.931
HMC_vs_DEMetro_Z 3 -16.586 3.94e-09 -4.788
HMC_vs_DEMetro_Z 4 -26.249 2.84e-11 -7.577
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.173 0.015 0.001 158.396
HMC 3.0 0.020 0.015 0.001 3.693
HMC 4.0 0.019 0.014 0.001 5.598
HMC 10.0 0.015 0.015 0.001 0.278
HMC 50.0 0.014 0.014 0.002 -0.345
SMC 2.1 0.405 0.015 0.001 390.953
SMC 3.0 0.417 0.015 0.001 295.980
SMC 4.0 0.421 0.014 0.001 435.426
SMC 10.0 0.383 0.015 0.001 298.961
SMC 50.0 0.091 0.014 0.002 47.903
Metro 2.1 0.097 0.015 0.001 82.876
Metro 3.0 0.056 0.015 0.001 30.151
Metro 4.0 0.045 0.014 0.001 33.265
Metro 10.0 0.030 0.015 0.001 12.314
Metro 50.0 0.025 0.014 0.002 6.486
DEMetro_Z 2.1 0.526 0.015 0.001 512.316
DEMetro_Z 3.0 0.465 0.015 0.001 331.008
DEMetro_Z 4.0 0.462 0.014 0.001 479.131
DEMetro_Z 10.0 0.381 0.015 0.001 297.622
DEMetro_Z 50.0 0.286 0.014 0.002 170.418
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Forest & Ridge Plots
Pooled
2.1 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
50 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2.1 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
50 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2.1
3
4
10
50
Chain
2.1
3
4
10
50

Varying_Tails_with_high_Correlation (MvStudentT, nu, 12 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -0.117 0.908 -0.054
HMC 3.0 1.165 0.261 0.764
HMC 4.0 0.919 0.372 0.660
HMC 10.0 0.704 0.49 0.379
HMC 50.0 2.296 0.0347 1.388
SMC 2.1 -2.008 0.0588 -0.699
SMC 3.0 1.580 0.128 0.687
SMC 4.0 0.842 0.409 0.314
SMC 10.0 -2.255 0.0366 -0.766
SMC 50.0 0.780 0.444 0.309
Metro 2.1 2.258 0.0399 1.763
Metro 3.0 2.296 0.0412 4.197
Metro 4.0 4.173 0.00135 6.599
Metro 10.0 3.565 0.00414 6.801
Metro 50.0 2.972 0.0119 4.595
DEMetro_Z 2.1 1.483 0.164 2.269
DEMetro_Z 3.0 2.270 0.0387 1.711
DEMetro_Z 4.0 4.299 0.000558 2.843
DEMetro_Z 10.0 2.728 0.0151 1.859
DEMetro_Z 50.0 3.042 0.00686 1.657
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -1.460 0.172 -0.421
HMC_vs_DEMetro_Z 1 -0.878 0.399 -0.253
HMC_vs_DEMetro_Z 2 -2.329 0.0399 -0.672
HMC_vs_DEMetro_Z 3 -2.268 0.0444 -0.655
HMC_vs_DEMetro_Z 4 -0.422 0.681 -0.122
Metro_vs_SMC 0 3.174 0.00886 0.916
Metro_vs_SMC 1 1.869 0.0885 0.539
Metro_vs_SMC 2 4.294 0.00127 1.240
Metro_vs_SMC 3 4.198 0.00149 1.212
Metro_vs_SMC 4 2.718 0.02 0.785
Metro_vs_DEMetro_Z 0 -0.270 0.792 -0.078
Metro_vs_DEMetro_Z 1 1.572 0.144 0.454
Metro_vs_DEMetro_Z 2 2.386 0.0361 0.689
Metro_vs_DEMetro_Z 3 2.445 0.0325 0.706
Metro_vs_DEMetro_Z 4 1.769 0.105 0.511
HMC_vs_Metro 0 -2.126 0.057 -0.614
HMC_vs_Metro 1 -1.601 0.138 -0.462
HMC_vs_Metro 2 -3.920 0.00239 -1.132
HMC_vs_Metro 3 -3.715 0.00341 -1.072
HMC_vs_Metro 4 -1.845 0.0921 -0.533
HMC_vs_SMC 0 1.578 0.143 0.455
HMC_vs_SMC 1 0.153 0.882 0.044
HMC_vs_SMC 2 0.508 0.622 0.147
HMC_vs_SMC 3 3.541 0.00462 1.022
HMC_vs_SMC 4 1.619 0.134 0.467
DEMetro_Z_vs_SMC 0 1.890 0.0854 0.546
DEMetro_Z_vs_SMC 1 1.354 0.203 0.391
DEMetro_Z_vs_SMC 2 3.998 0.0021 1.154
DEMetro_Z_vs_SMC 3 4.445 0.000987 1.283
DEMetro_Z_vs_SMC 4 2.729 0.0196 0.788
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.077 0.080 0.048 -0.054
HMC 3.0 0.039 0.025 0.018 0.764
HMC 4.0 0.037 0.026 0.016 0.660
HMC 10.0 0.027 0.022 0.013 0.379
HMC 50.0 0.032 0.015 0.013 1.388
SMC 2.1 0.046 0.080 0.048 -0.699
SMC 3.0 0.038 0.025 0.018 0.687
SMC 4.0 0.031 0.026 0.016 0.314
SMC 10.0 0.013 0.022 0.013 -0.766
SMC 50.0 0.019 0.015 0.013 0.309
Metro 2.1 0.165 0.080 0.048 1.763
Metro 3.0 0.101 0.025 0.018 4.197
Metro 4.0 0.134 0.026 0.016 6.599
Metro 10.0 0.110 0.022 0.013 6.801
Metro 50.0 0.073 0.015 0.013 4.595
DEMetro_Z 2.1 0.189 0.080 0.048 2.269
DEMetro_Z 3.0 0.056 0.025 0.018 1.711
DEMetro_Z 4.0 0.073 0.026 0.016 2.843
DEMetro_Z 10.0 0.046 0.022 0.013 1.859
DEMetro_Z 50.0 0.036 0.015 0.013 1.657
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.687 0.114 1.444
HMC 3.0 1.771 0.0989 1.565
HMC 4.0 2.356 0.0339 2.049
HMC 10.0 2.921 0.0118 2.837
HMC 50.0 3.231 0.00404 1.518
SMC 2.1 0.377 0.71 0.200
SMC 3.0 1.758 0.105 3.065
SMC 4.0 1.439 0.169 0.932
SMC 10.0 1.095 0.286 0.480
SMC 50.0 -0.212 0.834 -0.081
Metro 2.1 0.743 0.467 0.394
Metro 3.0 3.400 0.004 2.507
Metro 4.0 3.246 0.00678 3.911
Metro 10.0 1.817 0.0961 6.796
Metro 50.0 2.934 0.0117 2.970
DEMetro_Z 2.1 0.856 0.403 0.458
DEMetro_Z 3.0 2.541 0.0241 2.327
DEMetro_Z 4.0 3.262 0.00555 2.589
DEMetro_Z 10.0 2.848 0.0134 2.605
DEMetro_Z 50.0 2.261 0.0359 1.210
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 1.640 0.129 0.473
HMC_vs_SMC 1 -0.844 0.416 -0.244
HMC_vs_SMC 2 1.303 0.219 0.376
HMC_vs_SMC 3 2.660 0.0222 0.768
HMC_vs_SMC 4 4.017 0.00203 1.160
Metro_vs_DEMetro_Z 0 -0.595 0.564 -0.172
Metro_vs_DEMetro_Z 1 0.337 0.742 0.097
Metro_vs_DEMetro_Z 2 1.063 0.311 0.307
Metro_vs_DEMetro_Z 3 1.281 0.227 0.370
Metro_vs_DEMetro_Z 4 1.580 0.142 0.456
HMC_vs_Metro 0 1.400 0.189 0.404
HMC_vs_Metro 1 -1.204 0.254 -0.348
HMC_vs_Metro 2 -1.170 0.267 -0.338
HMC_vs_Metro 3 -1.030 0.325 -0.297
HMC_vs_Metro 4 -1.909 0.0826 -0.551
HMC_vs_DEMetro_Z 0 1.260 0.234 0.364
HMC_vs_DEMetro_Z 1 -1.057 0.313 -0.305
HMC_vs_DEMetro_Z 2 -0.511 0.62 -0.147
HMC_vs_DEMetro_Z 3 0.209 0.838 0.060
HMC_vs_DEMetro_Z 4 0.443 0.667 0.128
Metro_vs_SMC 0 3.695 0.00354 1.067
Metro_vs_SMC 1 -0.324 0.752 -0.093
Metro_vs_SMC 2 2.138 0.0558 0.617
Metro_vs_SMC 3 1.707 0.116 0.493
Metro_vs_SMC 4 3.065 0.0108 0.885
DEMetro_Z_vs_SMC 0 2.670 0.0218 0.771
DEMetro_Z_vs_SMC 1 -0.496 0.629 -0.143
DEMetro_Z_vs_SMC 2 1.834 0.0938 0.529
DEMetro_Z_vs_SMC 3 2.194 0.0506 0.633
DEMetro_Z_vs_SMC 4 2.586 0.0253 0.747
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 24.108 6.351 12.294 1.444
HMC 3.0 0.574 0.278 0.189 1.565
HMC 4.0 0.285 0.106 0.087 2.049
HMC 10.0 0.076 0.028 0.017 2.837
HMC 50.0 0.054 0.024 0.020 1.518
SMC 2.1 8.812 6.351 12.294 0.200
SMC 3.0 0.857 0.278 0.189 3.065
SMC 4.0 0.187 0.106 0.087 0.932
SMC 10.0 0.036 0.028 0.017 0.480
SMC 50.0 0.022 0.024 0.020 -0.081
Metro 2.1 11.195 6.351 12.294 0.394
Metro 3.0 0.752 0.278 0.189 2.507
Metro 4.0 0.447 0.106 0.087 3.911
Metro 10.0 0.143 0.028 0.017 6.796
Metro 50.0 0.082 0.024 0.020 2.970
DEMetro_Z 2.1 11.979 6.351 12.294 0.458
DEMetro_Z 3.0 0.718 0.278 0.189 2.327
DEMetro_Z 4.0 0.332 0.106 0.087 2.589
DEMetro_Z 10.0 0.072 0.028 0.017 2.605
DEMetro_Z 50.0 0.048 0.024 0.020 1.210
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.240 0.0454 3.786
HMC 3.0 4.572 0.000353 3.232
HMC 4.0 3.334 0.00444 2.350
HMC 10.0 3.236 0.00462 1.832
HMC 50.0 3.658 0.00211 2.383
SMC 2.1 -0.036 0.972 -0.016
SMC 3.0 1.479 0.158 0.956
SMC 4.0 0.416 0.682 0.144
SMC 10.0 -1.941 0.0657 -0.725
SMC 50.0 0.568 0.576 0.226
Metro 2.1 6.918 5.82e-06 5.307
Metro 3.0 6.544 3.56e-05 14.676
Metro 4.0 5.005 0.000355 10.321
Metro 10.0 4.000 0.00202 12.632
Metro 50.0 3.568 0.00421 8.346
DEMetro_Z 2.1 3.100 0.00949 5.280
DEMetro_Z 3.0 5.643 0.00011 8.023
DEMetro_Z 4.0 5.899 4.47e-05 5.278
DEMetro_Z 10.0 4.319 0.000713 3.601
DEMetro_Z 50.0 6.136 7.92e-06 3.374
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 0.013 0.99 0.004
Metro_vs_DEMetro_Z 1 3.329 0.00672 0.961
Metro_vs_DEMetro_Z 2 2.159 0.0538 0.623
Metro_vs_DEMetro_Z 3 2.991 0.0123 0.863
Metro_vs_DEMetro_Z 4 1.970 0.0745 0.569
DEMetro_Z_vs_SMC 0 3.021 0.0116 0.872
DEMetro_Z_vs_SMC 1 4.903 0.00047 1.415
DEMetro_Z_vs_SMC 2 6.232 6.42e-05 1.799
DEMetro_Z_vs_SMC 3 5.088 0.000351 1.469
DEMetro_Z_vs_SMC 4 5.843 0.000112 1.687
HMC_vs_DEMetro_Z 0 -0.551 0.593 -0.159
HMC_vs_DEMetro_Z 1 -3.547 0.00458 -1.024
HMC_vs_DEMetro_Z 2 -3.742 0.00325 -1.080
HMC_vs_DEMetro_Z 3 -2.172 0.0526 -0.627
HMC_vs_DEMetro_Z 4 -1.548 0.15 -0.447
HMC_vs_Metro 0 -0.812 0.434 -0.235
HMC_vs_Metro 1 -4.650 0.000705 -1.342
HMC_vs_Metro 2 -3.778 0.00306 -1.090
HMC_vs_Metro 3 -3.558 0.00448 -1.027
HMC_vs_Metro 4 -2.535 0.0277 -0.732
HMC_vs_SMC 0 2.206 0.0496 0.637
HMC_vs_SMC 1 3.776 0.00307 1.090
HMC_vs_SMC 2 3.573 0.00437 1.031
HMC_vs_SMC 3 5.121 0.000333 1.478
HMC_vs_SMC 4 3.050 0.011 0.881
Metro_vs_SMC 0 10.833 3.3e-07 3.127
Metro_vs_SMC 1 6.271 6.08e-05 1.810
Metro_vs_SMC 2 4.925 0.000453 1.422
Metro_vs_SMC 3 4.285 0.00129 1.237
Metro_vs_SMC 4 3.380 0.00614 0.976
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.273 0.119 0.041 3.786
HMC 3.0 0.086 0.058 0.008 3.232
HMC 4.0 0.073 0.046 0.012 2.350
HMC 10.0 0.045 0.032 0.007 1.832
HMC 50.0 0.042 0.024 0.007 2.383
SMC 2.1 0.118 0.119 0.041 -0.016
SMC 3.0 0.067 0.058 0.008 0.956
SMC 4.0 0.048 0.046 0.012 0.144
SMC 10.0 0.027 0.032 0.007 -0.725
SMC 50.0 0.026 0.024 0.007 0.226
Metro 2.1 0.335 0.119 0.041 5.307
Metro 3.0 0.183 0.058 0.008 14.676
Metro 4.0 0.166 0.046 0.012 10.321
Metro 10.0 0.120 0.032 0.007 12.632
Metro 50.0 0.086 0.024 0.007 8.346
DEMetro_Z 2.1 0.334 0.119 0.041 5.280
DEMetro_Z 3.0 0.126 0.058 0.008 8.023
DEMetro_Z 4.0 0.107 0.046 0.012 5.278
DEMetro_Z 10.0 0.057 0.032 0.007 3.601
DEMetro_Z 50.0 0.049 0.024 0.007 3.374
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 4.061 0.000633 2.061
HMC 3.0 3.340 0.00356 1.828
HMC 4.0 2.775 0.0129 1.656
HMC 10.0 2.637 0.0167 1.477
HMC 50.0 4.515 0.000186 2.052
SMC 2.1 1.034 0.318 0.793
SMC 3.0 0.336 0.74 0.172
SMC 4.0 -0.697 0.494 -0.260
SMC 10.0 -1.794 0.0869 -0.691
SMC 50.0 0.442 0.663 0.166
Metro 2.1 6.931 1.54e-05 9.333
Metro 3.0 6.509 2.8e-05 8.660
Metro 4.0 3.442 0.00511 6.105
Metro 10.0 4.266 0.00113 6.475
Metro 50.0 4.384 0.00097 7.972
DEMetro_Z 2.1 5.284 0.00017 6.093
DEMetro_Z 3.0 6.831 3.46e-06 4.300
DEMetro_Z 4.0 3.828 0.00188 3.246
DEMetro_Z 10.0 3.106 0.00809 2.845
DEMetro_Z 50.0 4.027 0.00116 3.086
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 3.723 0.00337 1.075
DEMetro_Z_vs_SMC 1 5.549 0.000173 1.602
DEMetro_Z_vs_SMC 2 4.069 0.00186 1.175
DEMetro_Z_vs_SMC 3 3.644 0.00386 1.052
DEMetro_Z_vs_SMC 4 3.786 0.00302 1.093
HMC_vs_Metro 0 -5.756 0.000127 -1.662
HMC_vs_Metro 1 -5.190 0.000299 -1.498
HMC_vs_Metro 2 -2.399 0.0353 -0.692
HMC_vs_Metro 3 -3.586 0.00427 -1.035
HMC_vs_Metro 4 -3.436 0.00556 -0.992
Metro_vs_DEMetro_Z 0 1.828 0.0948 0.528
Metro_vs_DEMetro_Z 1 3.022 0.0116 0.872
Metro_vs_DEMetro_Z 2 1.477 0.168 0.426
Metro_vs_DEMetro_Z 3 2.135 0.0561 0.616
Metro_vs_DEMetro_Z 4 2.250 0.0459 0.649
HMC_vs_SMC 0 1.399 0.189 0.404
HMC_vs_SMC 1 3.322 0.0068 0.959
HMC_vs_SMC 2 4.566 0.000808 1.318
HMC_vs_SMC 3 3.995 0.0021 1.153
HMC_vs_SMC 4 4.023 0.00201 1.161
Metro_vs_SMC 0 7.614 1.04e-05 2.198
Metro_vs_SMC 1 7.769 8.62e-06 2.243
Metro_vs_SMC 2 3.500 0.00497 1.010
Metro_vs_SMC 3 4.810 0.000545 1.388
Metro_vs_SMC 4 4.339 0.00118 1.253
HMC_vs_DEMetro_Z 0 -3.153 0.00919 -0.910
HMC_vs_DEMetro_Z 1 -3.332 0.00669 -0.962
HMC_vs_DEMetro_Z 2 -1.941 0.0783 -0.560
HMC_vs_DEMetro_Z 3 -1.375 0.196 -0.397
HMC_vs_DEMetro_Z 4 -1.313 0.216 -0.379
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.026 0.015 0.005 2.061
HMC 3.0 0.022 0.014 0.004 1.828
HMC 4.0 0.024 0.015 0.005 1.656
HMC 10.0 0.021 0.014 0.004 1.477
HMC 50.0 0.021 0.012 0.004 2.052
SMC 2.1 0.019 0.015 0.005 0.793
SMC 3.0 0.015 0.014 0.004 0.172
SMC 4.0 0.014 0.015 0.005 -0.260
SMC 10.0 0.011 0.014 0.004 -0.691
SMC 50.0 0.013 0.012 0.004 0.166
Metro 2.1 0.064 0.015 0.005 9.333
Metro 3.0 0.049 0.014 0.004 8.660
Metro 4.0 0.048 0.015 0.005 6.105
Metro 10.0 0.042 0.014 0.004 6.475
Metro 50.0 0.046 0.012 0.004 7.972
DEMetro_Z 2.1 0.047 0.015 0.005 6.093
DEMetro_Z 3.0 0.032 0.014 0.004 4.300
DEMetro_Z 4.0 0.033 0.015 0.005 3.246
DEMetro_Z 10.0 0.027 0.014 0.004 2.845
DEMetro_Z 50.0 0.025 0.012 0.004 3.086
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -0.186 0.854 -0.086
HMC 3.0 1.477 0.16 1.075
HMC 4.0 2.606 0.0193 1.753
HMC 10.0 0.390 0.702 0.235
HMC 50.0 1.930 0.0716 1.265
SMC 2.1 -0.953 0.352 -0.334
SMC 3.0 1.111 0.281 0.601
SMC 4.0 -1.439 0.169 -0.466
SMC 10.0 -0.737 0.469 -0.280
SMC 50.0 0.111 0.912 0.041
Metro 2.1 2.660 0.0204 3.229
Metro 3.0 3.787 0.00265 5.662
Metro 4.0 3.780 0.0024 4.134
Metro 10.0 2.979 0.0114 3.910
Metro 50.0 5.154 0.000227 6.542
DEMetro_Z 2.1 1.901 0.0761 1.307
DEMetro_Z 3.0 3.360 0.00445 2.567
DEMetro_Z 4.0 2.575 0.0221 2.158
DEMetro_Z 10.0 2.717 0.0127 1.188
DEMetro_Z 50.0 1.594 0.132 1.192
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -1.785 0.102 -0.515
HMC_vs_DEMetro_Z 1 -1.274 0.229 -0.368
HMC_vs_DEMetro_Z 2 -0.383 0.709 -0.110
HMC_vs_DEMetro_Z 3 -1.836 0.0936 -0.530
HMC_vs_DEMetro_Z 4 0.074 0.942 0.021
Metro_vs_SMC 0 2.972 0.0127 0.858
Metro_vs_SMC 1 2.927 0.0138 0.845
Metro_vs_SMC 2 4.579 0.000792 1.322
Metro_vs_SMC 3 3.558 0.00449 1.027
Metro_vs_SMC 4 5.543 0.000174 1.600
Metro_vs_DEMetro_Z 0 1.689 0.119 0.488
Metro_vs_DEMetro_Z 1 2.240 0.0467 0.647
Metro_vs_DEMetro_Z 2 1.301 0.22 0.376
Metro_vs_DEMetro_Z 3 2.022 0.0681 0.584
Metro_vs_DEMetro_Z 4 3.382 0.00612 0.976
HMC_vs_Metro 0 -2.434 0.0332 -0.703
HMC_vs_Metro 1 -2.676 0.0216 -0.773
HMC_vs_Metro 2 -1.858 0.0901 -0.536
HMC_vs_Metro 3 -2.626 0.0236 -0.758
HMC_vs_Metro 4 -4.010 0.00205 -1.157
HMC_vs_SMC 0 0.797 0.442 0.230
HMC_vs_SMC 1 0.504 0.624 0.145
HMC_vs_SMC 2 3.710 0.00344 1.071
HMC_vs_SMC 3 0.932 0.372 0.269
HMC_vs_SMC 4 2.236 0.047 0.646
DEMetro_Z_vs_SMC 0 2.363 0.0376 0.682
DEMetro_Z_vs_SMC 1 2.485 0.0303 0.717
DEMetro_Z_vs_SMC 2 3.151 0.00922 0.910
DEMetro_Z_vs_SMC 3 3.073 0.0106 0.887
DEMetro_Z_vs_SMC 4 1.595 0.139 0.460
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.076 0.080 0.048 -0.086
HMC 3.0 0.045 0.025 0.018 1.075
HMC 4.0 0.055 0.026 0.016 1.753
HMC 10.0 0.025 0.022 0.013 0.235
HMC 50.0 0.031 0.015 0.013 1.265
SMC 2.1 0.064 0.080 0.048 -0.334
SMC 3.0 0.036 0.025 0.018 0.601
SMC 4.0 0.018 0.026 0.016 -0.466
SMC 10.0 0.019 0.022 0.013 -0.280
SMC 50.0 0.015 0.015 0.013 0.041
Metro 2.1 0.235 0.080 0.048 3.229
Metro 3.0 0.128 0.025 0.018 5.662
Metro 4.0 0.094 0.026 0.016 4.134
Metro 10.0 0.073 0.022 0.013 3.910
Metro 50.0 0.097 0.015 0.013 6.542
DEMetro_Z 2.1 0.143 0.080 0.048 1.307
DEMetro_Z 3.0 0.072 0.025 0.018 2.567
DEMetro_Z 4.0 0.061 0.026 0.016 2.158
DEMetro_Z 10.0 0.038 0.022 0.013 1.188
DEMetro_Z 50.0 0.030 0.015 0.013 1.192
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 0.510 0.616 0.264
HMC 3.0 1.664 0.12 1.764
HMC 4.0 1.272 0.221 0.814
HMC 10.0 2.298 0.0388 2.301
HMC 50.0 2.606 0.0163 1.151
SMC 2.1 0.456 0.653 0.240
SMC 3.0 1.153 0.263 0.599
SMC 4.0 0.543 0.593 0.221
SMC 10.0 0.534 0.599 0.270
SMC 50.0 1.614 0.121 0.648
Metro 2.1 0.668 0.512 0.344
Metro 3.0 1.857 0.0865 1.953
Metro 4.0 3.053 0.0097 3.611
Metro 10.0 4.473 0.000797 6.963
Metro 50.0 3.492 0.00428 4.238
DEMetro_Z 2.1 0.647 0.525 0.348
DEMetro_Z 3.0 3.036 0.0091 2.645
DEMetro_Z 4.0 3.733 0.00124 1.741
DEMetro_Z 10.0 2.938 0.0112 2.692
DEMetro_Z 50.0 1.936 0.071 1.294
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.638 0.536 0.184
HMC_vs_SMC 1 1.052 0.315 0.304
HMC_vs_SMC 2 1.009 0.335 0.291
HMC_vs_SMC 3 1.854 0.0907 0.535
HMC_vs_SMC 4 1.233 0.243 0.356
Metro_vs_DEMetro_Z 0 -0.060 0.953 -0.017
Metro_vs_DEMetro_Z 1 -0.717 0.488 -0.207
Metro_vs_DEMetro_Z 2 1.803 0.0988 0.521
Metro_vs_DEMetro_Z 3 2.663 0.0221 0.769
Metro_vs_DEMetro_Z 4 2.071 0.0627 0.598
HMC_vs_Metro 0 -1.038 0.322 -0.300
HMC_vs_Metro 1 -0.154 0.88 -0.045
HMC_vs_Metro 2 -2.461 0.0316 -0.710
HMC_vs_Metro 3 -2.375 0.0368 -0.686
HMC_vs_Metro 4 -2.968 0.0128 -0.857
HMC_vs_DEMetro_Z 0 -2.352 0.0384 -0.679
HMC_vs_DEMetro_Z 1 -0.933 0.371 -0.269
HMC_vs_DEMetro_Z 2 -1.526 0.155 -0.441
HMC_vs_DEMetro_Z 3 -0.337 0.743 -0.097
HMC_vs_DEMetro_Z 4 -0.232 0.821 -0.067
Metro_vs_SMC 0 1.829 0.0947 0.528
Metro_vs_SMC 1 1.317 0.215 0.380
Metro_vs_SMC 2 2.806 0.0171 0.810
Metro_vs_SMC 3 4.984 0.000413 1.439
Metro_vs_SMC 4 3.614 0.00407 1.043
DEMetro_Z_vs_SMC 0 3.111 0.00991 0.898
DEMetro_Z_vs_SMC 1 2.786 0.0177 0.804
DEMetro_Z_vs_SMC 2 3.622 0.00401 1.046
DEMetro_Z_vs_SMC 3 2.571 0.026 0.742
DEMetro_Z_vs_SMC 4 0.920 0.377 0.266
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 9.598 6.351 12.294 0.264
HMC 3.0 0.611 0.278 0.189 1.764
HMC 4.0 0.177 0.106 0.087 0.814
HMC 10.0 0.067 0.028 0.017 2.301
HMC 50.0 0.046 0.024 0.020 1.151
SMC 2.1 9.296 6.351 12.294 0.240
SMC 3.0 0.391 0.278 0.189 0.599
SMC 4.0 0.125 0.106 0.087 0.221
SMC 10.0 0.032 0.028 0.017 0.270
SMC 50.0 0.037 0.024 0.020 0.648
Metro 2.1 10.576 6.351 12.294 0.344
Metro 3.0 0.647 0.278 0.189 1.953
Metro 4.0 0.421 0.106 0.087 3.611
Metro 10.0 0.146 0.028 0.017 6.963
Metro 50.0 0.107 0.024 0.020 4.238
DEMetro_Z 2.1 10.634 6.351 12.294 0.348
DEMetro_Z 3.0 0.778 0.278 0.189 2.645
DEMetro_Z 4.0 0.258 0.106 0.087 1.741
DEMetro_Z 10.0 0.073 0.028 0.017 2.692
DEMetro_Z 50.0 0.049 0.024 0.020 1.294
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.694 0.105 0.815
HMC 3.0 3.159 0.00746 3.060
HMC 4.0 3.986 0.00113 2.757
HMC 10.0 1.439 0.172 1.166
HMC 50.0 3.727 0.00181 2.407
SMC 2.1 0.187 0.853 0.081
SMC 3.0 0.911 0.375 0.563
SMC 4.0 -1.196 0.247 -0.404
SMC 10.0 -0.892 0.382 -0.396
SMC 50.0 0.671 0.51 0.238
Metro 2.1 5.814 6.37e-05 6.045
Metro 3.0 7.490 9.73e-06 15.572
Metro 4.0 6.099 4.76e-05 7.365
Metro 10.0 6.278 3.97e-05 8.401
Metro 50.0 8.128 3.1e-06 10.949
DEMetro_Z 2.1 4.239 0.000855 3.636
DEMetro_Z 3.0 8.574 1.12e-06 8.818
DEMetro_Z 4.0 4.769 0.000304 3.986
DEMetro_Z 10.0 5.487 2.97e-05 2.980
DEMetro_Z 50.0 4.244 0.000808 3.464
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 1.913 0.0821 0.552
Metro_vs_DEMetro_Z 1 2.962 0.0129 0.855
Metro_vs_DEMetro_Z 2 1.865 0.089 0.538
Metro_vs_DEMetro_Z 3 4.007 0.00206 1.157
Metro_vs_DEMetro_Z 4 4.398 0.00107 1.270
DEMetro_Z_vs_SMC 0 4.151 0.00161 1.198
DEMetro_Z_vs_SMC 1 8.360 4.29e-06 2.413
DEMetro_Z_vs_SMC 2 5.550 0.000173 1.602
DEMetro_Z_vs_SMC 3 5.483 0.000191 1.583
DEMetro_Z_vs_SMC 4 4.015 0.00203 1.159
HMC_vs_DEMetro_Z 0 -3.012 0.0118 -0.869
HMC_vs_DEMetro_Z 1 -5.669 0.000145 -1.636
HMC_vs_DEMetro_Z 2 -1.088 0.3 -0.314
HMC_vs_DEMetro_Z 3 -2.290 0.0428 -0.661
HMC_vs_DEMetro_Z 4 -1.218 0.249 -0.352
HMC_vs_Metro 0 -4.985 0.000412 -1.439
HMC_vs_Metro 1 -4.914 0.000461 -1.419
HMC_vs_Metro 2 -3.649 0.00383 -1.053
HMC_vs_Metro 3 -4.315 0.00122 -1.246
HMC_vs_Metro 4 -6.634 3.69e-05 -1.915
HMC_vs_SMC 0 3.172 0.00889 0.916
HMC_vs_SMC 1 2.100 0.0596 0.606
HMC_vs_SMC 2 4.280 0.0013 1.235
HMC_vs_SMC 3 1.710 0.115 0.494
HMC_vs_SMC 4 3.931 0.00235 1.135
Metro_vs_SMC 0 5.862 0.000109 1.692
Metro_vs_SMC 1 6.718 3.3e-05 1.939
Metro_vs_SMC 2 6.470 4.62e-05 1.868
Metro_vs_SMC 3 7.558 1.12e-05 2.182
Metro_vs_SMC 4 8.726 2.83e-06 2.519
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.152 0.119 0.041 0.815
HMC 3.0 0.084 0.058 0.008 3.060
HMC 4.0 0.078 0.046 0.012 2.757
HMC 10.0 0.040 0.032 0.007 1.166
HMC 50.0 0.042 0.024 0.007 2.407
SMC 2.1 0.122 0.119 0.041 0.081
SMC 3.0 0.063 0.058 0.008 0.563
SMC 4.0 0.041 0.046 0.012 -0.404
SMC 10.0 0.029 0.032 0.007 -0.396
SMC 50.0 0.026 0.024 0.007 0.238
Metro 2.1 0.365 0.119 0.041 6.045
Metro 3.0 0.190 0.058 0.008 15.572
Metro 4.0 0.132 0.046 0.012 7.365
Metro 10.0 0.091 0.032 0.007 8.401
Metro 50.0 0.105 0.024 0.007 10.949
DEMetro_Z 2.1 0.267 0.119 0.041 3.636
DEMetro_Z 3.0 0.133 0.058 0.008 8.818
DEMetro_Z 4.0 0.092 0.046 0.012 3.986
DEMetro_Z 10.0 0.053 0.032 0.007 2.980
DEMetro_Z 50.0 0.050 0.024 0.007 3.464
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.773 0.0942 1.075
HMC 3.0 1.656 0.115 0.948
HMC 4.0 3.023 0.00739 1.727
HMC 10.0 1.240 0.231 0.677
HMC 50.0 4.307 0.000406 2.355
SMC 2.1 0.359 0.723 0.126
SMC 3.0 0.157 0.877 0.086
SMC 4.0 -1.383 0.181 -0.514
SMC 10.0 -0.811 0.426 -0.332
SMC 50.0 0.689 0.499 0.241
Metro 2.1 6.927 1.71e-05 10.474
Metro 3.0 7.270 9.59e-06 9.774
Metro 4.0 5.740 5.13e-05 4.751
Metro 10.0 8.393 8.66e-07 7.161
Metro 50.0 7.914 4.2e-06 10.936
DEMetro_Z 2.1 3.263 0.00706 5.650
DEMetro_Z 3.0 5.176 0.000182 5.249
DEMetro_Z 4.0 3.280 0.00531 2.564
DEMetro_Z 10.0 4.488 0.000357 2.869
DEMetro_Z 50.0 3.831 0.00177 3.027
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 3.269 0.00748 0.944
DEMetro_Z_vs_SMC 1 5.341 0.000237 1.542
DEMetro_Z_vs_SMC 2 4.331 0.00119 1.250
DEMetro_Z_vs_SMC 3 4.615 0.000747 1.332
DEMetro_Z_vs_SMC 4 3.489 0.00506 1.007
HMC_vs_Metro 0 -5.726 0.000133 -1.653
HMC_vs_Metro 1 -6.977 2.34e-05 -2.014
HMC_vs_Metro 2 -3.442 0.00551 -0.993
HMC_vs_Metro 3 -6.977 2.34e-05 -2.014
HMC_vs_Metro 4 -6.152 7.19e-05 -1.776
Metro_vs_DEMetro_Z 0 2.256 0.0454 0.651
Metro_vs_DEMetro_Z 1 2.804 0.0172 0.809
Metro_vs_DEMetro_Z 2 1.540 0.152 0.444
Metro_vs_DEMetro_Z 3 5.453 0.0002 1.574
Metro_vs_DEMetro_Z 4 4.622 0.000739 1.334
HMC_vs_SMC 0 2.233 0.0473 0.645
HMC_vs_SMC 1 1.308 0.218 0.378
HMC_vs_SMC 2 3.620 0.00402 1.045
HMC_vs_SMC 3 1.562 0.147 0.451
HMC_vs_SMC 4 4.438 0.000999 1.281
Metro_vs_SMC 0 6.729 3.25e-05 1.942
Metro_vs_SMC 1 7.769 8.63e-06 2.243
Metro_vs_SMC 2 6.202 6.7e-05 1.790
Metro_vs_SMC 3 9.380 1.4e-06 2.708
Metro_vs_SMC 4 8.314 4.52e-06 2.400
HMC_vs_DEMetro_Z 0 -2.472 0.031 -0.713
HMC_vs_DEMetro_Z 1 -4.431 0.00101 -1.279
HMC_vs_DEMetro_Z 2 -0.900 0.388 -0.260
HMC_vs_DEMetro_Z 3 -3.611 0.00409 -1.043
HMC_vs_DEMetro_Z 4 -1.033 0.324 -0.298
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.021 0.015 0.005 1.075
HMC 3.0 0.018 0.014 0.004 0.948
HMC 4.0 0.025 0.015 0.005 1.727
HMC 10.0 0.017 0.014 0.004 0.677
HMC 50.0 0.022 0.012 0.004 2.355
SMC 2.1 0.016 0.015 0.005 0.126
SMC 3.0 0.014 0.014 0.004 0.086
SMC 4.0 0.013 0.015 0.005 -0.514
SMC 10.0 0.013 0.014 0.004 -0.332
SMC 50.0 0.013 0.012 0.004 0.241
Metro 2.1 0.070 0.015 0.005 10.474
Metro 3.0 0.054 0.014 0.004 9.774
Metro 4.0 0.041 0.015 0.005 4.751
Metro 10.0 0.045 0.014 0.004 7.161
Metro 50.0 0.059 0.012 0.004 10.936
DEMetro_Z 2.1 0.045 0.015 0.005 5.650
DEMetro_Z 3.0 0.036 0.014 0.004 5.249
DEMetro_Z 4.0 0.029 0.015 0.005 2.564
DEMetro_Z 10.0 0.027 0.014 0.004 2.869
DEMetro_Z 50.0 0.025 0.012 0.004 3.027
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
2.1 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
50 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2.1 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
50 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2.1
3
4
10
50
Chain
2.1
3
4
10
50

Vary_Tails_with_high_Multimodality (Mixture, nu, 12 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 4.549 0.000782 11.953
HMC 3.0 5.179 0.00027 11.007
HMC 4.0 3.583 0.00424 15.656
HMC 10.0 6.962 2.31e-05 36.838
HMC 50.0 4.896 0.000468 30.587
SMC 2.1 3.450 0.0052 7.994
SMC 3.0 2.318 0.0346 1.621
SMC 4.0 2.082 0.0494 0.916
SMC 10.0 -0.909 0.375 -0.303
SMC 50.0 1.772 0.0923 0.928
Metro 2.1 3.611 0.00379 6.681
Metro 3.0 3.236 0.00769 8.367
Metro 4.0 4.069 0.00181 14.391
Metro 10.0 4.513 0.000874 29.963
Metro 50.0 5.723 0.000131 36.638
DEMetro_Z 2.1 2.739 0.0191 10.304
DEMetro_Z 3.0 5.476 0.000184 19.220
DEMetro_Z 4.0 4.883 0.000473 22.668
DEMetro_Z 10.0 3.702 0.00346 21.450
DEMetro_Z 50.0 3.565 0.00441 25.162
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 0.336 0.743 0.097
HMC_vs_DEMetro_Z 1 -2.320 0.0406 -0.670
HMC_vs_DEMetro_Z 2 -1.004 0.337 -0.290
HMC_vs_DEMetro_Z 3 2.561 0.0265 0.739
HMC_vs_DEMetro_Z 4 0.653 0.527 0.188
Metro_vs_SMC 0 -0.503 0.625 -0.145
Metro_vs_SMC 1 2.268 0.0445 0.655
Metro_vs_SMC 2 3.780 0.00305 1.091
Metro_vs_SMC 3 4.536 0.000849 1.309
Metro_vs_SMC 4 5.616 0.000157 1.621
Metro_vs_DEMetro_Z 0 -0.778 0.453 -0.224
Metro_vs_DEMetro_Z 1 -2.341 0.0391 -0.676
Metro_vs_DEMetro_Z 2 -1.618 0.134 -0.467
Metro_vs_DEMetro_Z 3 1.287 0.225 0.372
Metro_vs_DEMetro_Z 4 1.597 0.138 0.461
HMC_vs_Metro 0 1.770 0.104 0.511
HMC_vs_Metro 1 0.810 0.435 0.234
HMC_vs_Metro 2 0.246 0.81 0.071
HMC_vs_Metro 3 1.187 0.26 0.343
HMC_vs_Metro 4 -0.816 0.432 -0.236
HMC_vs_SMC 0 0.971 0.352 0.280
HMC_vs_SMC 1 4.036 0.00196 1.165
HMC_vs_SMC 2 3.297 0.00712 0.952
HMC_vs_SMC 3 7.084 2.03e-05 2.045
HMC_vs_SMC 4 4.898 0.000473 1.414
DEMetro_Z_vs_SMC 0 0.511 0.619 0.147
DEMetro_Z_vs_SMC 1 5.114 0.000337 1.476
DEMetro_Z_vs_SMC 2 4.874 0.000491 1.407
DEMetro_Z_vs_SMC 3 3.736 0.00329 1.079
DEMetro_Z_vs_SMC 4 3.547 0.00458 1.024
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.830 0.066 0.064 11.953
HMC 3.0 1.019 0.091 0.084 11.007
HMC 4.0 1.489 0.079 0.090 15.656
HMC 10.0 3.013 0.091 0.079 36.838
HMC 50.0 2.437 0.096 0.077 30.587
SMC 2.1 0.577 0.066 0.064 7.994
SMC 3.0 0.227 0.091 0.084 1.621
SMC 4.0 0.162 0.079 0.090 0.916
SMC 10.0 0.067 0.091 0.079 -0.303
SMC 50.0 0.167 0.096 0.077 0.928
Metro 2.1 0.493 0.066 0.064 6.681
Metro 3.0 0.796 0.091 0.084 8.367
Metro 4.0 1.375 0.079 0.090 14.391
Metro 10.0 2.467 0.091 0.079 29.963
Metro 50.0 2.900 0.096 0.077 36.638
DEMetro_Z 2.1 0.724 0.066 0.064 10.304
DEMetro_Z 3.0 1.712 0.091 0.084 19.220
DEMetro_Z 4.0 2.120 0.079 0.090 22.668
DEMetro_Z 10.0 1.792 0.091 0.079 21.450
DEMetro_Z 50.0 2.022 0.096 0.077 25.162
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -1.448 0.175 -0.420
HMC 3.0 1.431 0.177 1.622
HMC 4.0 1.881 0.0867 40.404
HMC 10.0 3.864 0.00263 66.613
HMC 50.0 3.258 0.00762 69.392
SMC 2.1 -1.456 0.173 -0.422
SMC 3.0 -0.160 0.875 -0.049
SMC 4.0 0.903 0.379 0.520
SMC 10.0 -0.300 0.767 -0.106
SMC 50.0 -0.653 0.52 -0.265
Metro 2.1 -1.541 0.151 -0.446
Metro 3.0 1.465 0.169 2.135
Metro 4.0 2.889 0.0147 31.152
Metro 10.0 2.887 0.0148 55.230
Metro 50.0 3.505 0.00492 92.946
DEMetro_Z 2.1 -1.454 0.174 -0.421
DEMetro_Z 3.0 2.570 0.0258 8.693
DEMetro_Z 4.0 2.364 0.0375 65.619
DEMetro_Z 10.0 2.682 0.0213 33.263
DEMetro_Z 50.0 2.398 0.0354 59.844
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.048 0.962 0.014
HMC_vs_SMC 1 1.476 0.168 0.426
HMC_vs_SMC 2 1.876 0.0874 0.542
HMC_vs_SMC 3 3.862 0.00264 1.115
HMC_vs_SMC 4 3.284 0.00728 0.948
Metro_vs_DEMetro_Z 0 -1.129 0.283 -0.326
Metro_vs_DEMetro_Z 1 -1.682 0.121 -0.486
Metro_vs_DEMetro_Z 2 -1.135 0.281 -0.328
Metro_vs_DEMetro_Z 3 1.279 0.227 0.369
Metro_vs_DEMetro_Z 4 1.130 0.282 0.326
HMC_vs_Metro 0 0.796 0.443 0.230
HMC_vs_Metro 1 -0.266 0.795 -0.077
HMC_vs_Metro 2 0.376 0.714 0.108
HMC_vs_Metro 3 0.615 0.551 0.178
HMC_vs_Metro 4 -0.940 0.367 -0.271
HMC_vs_DEMetro_Z 0 0.022 0.983 0.006
HMC_vs_DEMetro_Z 1 -2.049 0.0651 -0.592
HMC_vs_DEMetro_Z 2 -0.648 0.53 -0.187
HMC_vs_DEMetro_Z 3 2.360 0.0378 0.681
HMC_vs_DEMetro_Z 4 0.301 0.769 0.087
Metro_vs_SMC 0 -0.782 0.451 -0.226
Metro_vs_SMC 1 1.538 0.152 0.444
Metro_vs_SMC 2 2.852 0.0157 0.823
Metro_vs_SMC 3 2.900 0.0144 0.837
Metro_vs_SMC 4 3.517 0.00483 1.015
DEMetro_Z_vs_SMC 0 0.028 0.979 0.008
DEMetro_Z_vs_SMC 1 2.558 0.0266 0.739
DEMetro_Z_vs_SMC 2 2.342 0.039 0.676
DEMetro_Z_vs_SMC 3 2.694 0.0209 0.778
DEMetro_Z_vs_SMC 4 2.398 0.0353 0.692
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 5.258 26.699 51.062 -0.420
HMC 3.0 1.752 0.764 0.609 1.622
HMC 4.0 5.544 0.284 0.130 40.404
HMC 10.0 16.071 0.283 0.237 66.613
HMC 50.0 11.326 0.268 0.159 69.392
SMC 2.1 5.167 26.699 51.062 -0.422
SMC 3.0 0.734 0.764 0.609 -0.049
SMC 4.0 0.352 0.284 0.130 0.520
SMC 10.0 0.258 0.283 0.237 -0.106
SMC 50.0 0.226 0.268 0.159 -0.265
Metro 2.1 3.938 26.699 51.062 -0.446
Metro 3.0 2.064 0.764 0.609 2.135
Metro 4.0 4.340 0.284 0.130 31.152
Metro 10.0 13.374 0.283 0.237 55.230
Metro 50.0 15.080 0.268 0.159 92.946
DEMetro_Z 2.1 5.219 26.699 51.062 -0.421
DEMetro_Z 3.0 6.059 0.764 0.609 8.693
DEMetro_Z 4.0 8.827 0.284 0.130 65.619
DEMetro_Z 10.0 8.167 0.283 0.237 33.263
DEMetro_Z 50.0 9.805 0.268 0.159 59.844
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 3.983 0.00192 6.783
HMC 3.0 5.153 0.000283 11.193
HMC 4.0 3.580 0.00428 17.675
HMC 10.0 6.561 3.97e-05 36.506
HMC 50.0 5.032 0.000378 33.687
SMC 2.1 5.856 5.9e-05 6.053
SMC 3.0 3.189 0.00583 2.157
SMC 4.0 2.251 0.035 1.002
SMC 10.0 -1.087 0.292 -0.355
SMC 50.0 1.902 0.0726 1.013
Metro 2.1 4.006 0.00149 3.970
Metro 3.0 3.417 0.00556 8.795
Metro 4.0 4.262 0.0013 16.094
Metro 10.0 4.474 0.000931 29.512
Metro 50.0 5.520 0.000179 39.642
DEMetro_Z 2.1 2.909 0.0138 6.548
DEMetro_Z 3.0 5.169 0.000299 20.651
DEMetro_Z 4.0 4.749 0.000592 25.500
DEMetro_Z 10.0 3.577 0.00431 21.774
DEMetro_Z 50.0 3.499 0.00496 27.497
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -0.932 0.371 -0.269
Metro_vs_DEMetro_Z 1 -2.362 0.0377 -0.682
Metro_vs_DEMetro_Z 2 -1.741 0.109 -0.503
Metro_vs_DEMetro_Z 3 1.175 0.265 0.339
Metro_vs_DEMetro_Z 4 1.408 0.187 0.407
DEMetro_Z_vs_SMC 0 0.188 0.854 0.054
DEMetro_Z_vs_SMC 1 4.764 0.000586 1.375
DEMetro_Z_vs_SMC 2 4.740 0.000609 1.368
DEMetro_Z_vs_SMC 3 3.622 0.00401 1.046
DEMetro_Z_vs_SMC 4 3.478 0.00517 1.004
HMC_vs_DEMetro_Z 0 0.078 0.94 0.022
HMC_vs_DEMetro_Z 1 -2.339 0.0393 -0.675
HMC_vs_DEMetro_Z 2 -0.989 0.344 -0.286
HMC_vs_DEMetro_Z 3 2.348 0.0386 0.678
HMC_vs_DEMetro_Z 4 0.684 0.508 0.198
HMC_vs_Metro 0 1.536 0.153 0.444
HMC_vs_Metro 1 0.740 0.475 0.214
HMC_vs_Metro 2 0.281 0.784 0.081
HMC_vs_Metro 3 1.152 0.274 0.333
HMC_vs_Metro 4 -0.732 0.479 -0.211
HMC_vs_SMC 0 0.351 0.732 0.101
HMC_vs_SMC 1 3.821 0.00284 1.103
HMC_vs_SMC 2 3.310 0.00695 0.956
HMC_vs_SMC 3 6.683 3.45e-05 1.929
HMC_vs_SMC 4 5.056 0.000369 1.460
Metro_vs_SMC 0 -1.660 0.125 -0.479
Metro_vs_SMC 1 2.272 0.0442 0.656
Metro_vs_SMC 2 3.997 0.0021 1.154
Metro_vs_SMC 3 4.519 0.000874 1.304
Metro_vs_SMC 4 5.421 0.00021 1.565
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.843 0.182 0.098 6.783
HMC 3.0 0.913 0.130 0.070 11.193
HMC 4.0 1.360 0.108 0.071 17.675
HMC 10.0 2.719 0.110 0.071 36.506
HMC 50.0 2.192 0.106 0.062 33.687
SMC 2.1 0.772 0.182 0.098 6.053
SMC 3.0 0.281 0.130 0.070 2.157
SMC 4.0 0.179 0.108 0.071 1.002
SMC 10.0 0.085 0.110 0.071 -0.355
SMC 50.0 0.169 0.106 0.062 1.013
Metro 2.1 0.569 0.182 0.098 3.970
Metro 3.0 0.745 0.130 0.070 8.795
Metro 4.0 1.248 0.108 0.071 16.094
Metro 10.0 2.220 0.110 0.071 29.512
Metro 50.0 2.561 0.106 0.062 39.642
DEMetro_Z 2.1 0.821 0.182 0.098 6.548
DEMetro_Z 3.0 1.574 0.130 0.070 20.651
DEMetro_Z 4.0 1.914 0.108 0.071 25.500
DEMetro_Z 10.0 1.667 0.110 0.071 21.774
DEMetro_Z 50.0 1.809 0.106 0.062 27.497
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 4.191 0.00145 12.652
HMC 3.0 4.651 0.000664 12.791
HMC 4.0 3.564 0.00439 17.553
HMC 10.0 7.449 1.24e-05 39.741
HMC 50.0 5.105 0.000337 34.538
SMC 2.1 3.933 0.0022 8.983
SMC 3.0 2.724 0.015 1.796
SMC 4.0 2.078 0.0498 0.918
SMC 10.0 -0.790 0.44 -0.268
SMC 50.0 1.903 0.0725 1.013
Metro 2.1 3.799 0.00273 7.342
Metro 3.0 2.942 0.0132 9.748
Metro 4.0 4.090 0.00175 16.349
Metro 10.0 4.661 0.000686 32.534
Metro 50.0 5.896 0.000102 41.491
DEMetro_Z 2.1 2.694 0.0207 11.748
DEMetro_Z 3.0 5.077 0.000349 23.989
DEMetro_Z 4.0 5.064 0.000357 25.789
DEMetro_Z 10.0 3.709 0.00342 23.729
DEMetro_Z 50.0 3.754 0.00317 28.413
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 0.542 0.599 0.156
DEMetro_Z_vs_SMC 1 4.681 0.000671 1.351
DEMetro_Z_vs_SMC 2 5.044 0.000376 1.456
DEMetro_Z_vs_SMC 3 3.730 0.00332 1.077
DEMetro_Z_vs_SMC 4 3.749 0.00322 1.082
HMC_vs_Metro 0 1.599 0.138 0.462
HMC_vs_Metro 1 0.738 0.476 0.213
HMC_vs_Metro 2 0.206 0.841 0.059
HMC_vs_Metro 3 1.182 0.262 0.341
HMC_vs_Metro 4 -0.834 0.422 -0.241
Metro_vs_DEMetro_Z 0 -0.825 0.427 -0.238
Metro_vs_DEMetro_Z 1 -2.374 0.0369 -0.685
Metro_vs_DEMetro_Z 2 -1.700 0.117 -0.491
Metro_vs_DEMetro_Z 3 1.205 0.254 0.348
Metro_vs_DEMetro_Z 4 1.704 0.117 0.492
HMC_vs_SMC 0 0.827 0.426 0.239
HMC_vs_SMC 1 3.701 0.0035 1.068
HMC_vs_SMC 2 3.317 0.00687 0.958
HMC_vs_SMC 3 7.565 1.11e-05 2.184
HMC_vs_SMC 4 5.135 0.000326 1.482
Metro_vs_SMC 0 -0.610 0.554 -0.176
Metro_vs_SMC 1 2.158 0.0539 0.623
Metro_vs_SMC 2 3.837 0.00276 1.108
Metro_vs_SMC 3 4.671 0.000682 1.348
Metro_vs_SMC 4 5.832 0.000114 1.683
HMC_vs_DEMetro_Z 0 0.162 0.874 0.047
HMC_vs_DEMetro_Z 1 -2.383 0.0363 -0.688
HMC_vs_DEMetro_Z 2 -1.073 0.306 -0.310
HMC_vs_DEMetro_Z 3 2.408 0.0347 0.695
HMC_vs_DEMetro_Z 4 0.686 0.507 0.198
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.082 0.009 0.006 12.652
HMC 3.0 0.110 0.010 0.008 12.791
HMC 4.0 0.167 0.009 0.009 17.553
HMC 10.0 0.339 0.010 0.008 39.741
HMC 50.0 0.278 0.010 0.008 34.538
SMC 2.1 0.061 0.009 0.006 8.983
SMC 3.0 0.024 0.010 0.008 1.796
SMC 4.0 0.017 0.009 0.009 0.918
SMC 10.0 0.008 0.010 0.008 -0.268
SMC 50.0 0.018 0.010 0.008 1.013
Metro 2.1 0.051 0.009 0.006 7.342
Metro 3.0 0.086 0.010 0.008 9.748
Metro 4.0 0.156 0.009 0.009 16.349
Metro 10.0 0.279 0.010 0.008 32.534
Metro 50.0 0.332 0.010 0.008 41.491
DEMetro_Z 2.1 0.077 0.009 0.006 11.748
DEMetro_Z 3.0 0.197 0.010 0.008 23.989
DEMetro_Z 4.0 0.241 0.009 0.009 25.789
DEMetro_Z 10.0 0.207 0.010 0.008 23.729
DEMetro_Z 50.0 0.230 0.010 0.008 28.413
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 4.142 0.00156 11.270
HMC 3.0 6.560 3.5e-05 14.852
HMC 4.0 5.270 0.00026 28.756
HMC 10.0 24.746 3.61e-11 66.559
HMC 50.0 131.836 6.54e-29 71.808
SMC 2.1 3.292 0.00705 10.959
SMC 3.0 1.062 0.301 0.507
SMC 4.0 -0.232 0.82 -0.074
SMC 10.0 0.834 0.413 0.320
SMC 50.0 0.868 0.395 0.352
Metro 2.1 4.434 0.000699 4.636
Metro 3.0 1.780 0.102 8.708
Metro 4.0 2.310 0.0412 11.986
Metro 10.0 20.144 3.91e-10 66.162
Metro 50.0 140.408 9.21e-31 71.590
DEMetro_Z 2.1 2.995 0.0122 24.150
DEMetro_Z 3.0 2.953 0.0131 18.755
DEMetro_Z 4.0 2.914 0.014 21.786
DEMetro_Z 10.0 3.098 0.0101 31.137
DEMetro_Z 50.0 7.786 8.31e-06 61.054
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -1.415 0.185 -0.409
HMC_vs_DEMetro_Z 1 -0.571 0.579 -0.165
HMC_vs_DEMetro_Z 2 0.627 0.543 0.181
HMC_vs_DEMetro_Z 3 3.716 0.00341 1.073
HMC_vs_DEMetro_Z 4 1.355 0.203 0.391
Metro_vs_SMC 0 -1.739 0.11 -0.502
Metro_vs_SMC 1 1.664 0.124 0.480
Metro_vs_SMC 2 2.346 0.0387 0.677
Metro_vs_SMC 3 19.218 8.19e-10 5.548
Metro_vs_SMC 4 126.155 9.72e-19 36.418
Metro_vs_DEMetro_Z 0 -2.385 0.0362 -0.689
Metro_vs_DEMetro_Z 1 -1.092 0.298 -0.315
Metro_vs_DEMetro_Z 2 -0.955 0.36 -0.276
Metro_vs_DEMetro_Z 3 3.037 0.0113 0.877
Metro_vs_DEMetro_Z 4 1.364 0.2 0.394
HMC_vs_Metro 0 2.808 0.017 0.810
HMC_vs_Metro 1 0.957 0.359 0.276
HMC_vs_Metro 2 3.446 0.00546 0.995
HMC_vs_Metro 3 0.091 0.929 0.026
HMC_vs_Metro 4 0.811 0.435 0.234
HMC_vs_SMC 0 0.089 0.93 0.026
HMC_vs_SMC 1 6.366 5.33e-05 1.838
HMC_vs_SMC 2 5.322 0.000244 1.536
HMC_vs_SMC 3 25.625 3.69e-11 7.397
HMC_vs_SMC 4 118.205 1.99e-18 34.123
DEMetro_Z_vs_SMC 0 1.752 0.108 0.506
DEMetro_Z_vs_SMC 1 2.846 0.0159 0.822
DEMetro_Z_vs_SMC 2 2.921 0.0139 0.843
DEMetro_Z_vs_SMC 3 3.083 0.0104 0.890
DEMetro_Z_vs_SMC 4 7.750 8.82e-06 2.237
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.786 0.066 0.064 11.270
HMC 3.0 1.343 0.091 0.084 14.852
HMC 4.0 2.668 0.079 0.090 28.756
HMC 10.0 5.370 0.091 0.079 66.559
HMC 50.0 5.591 0.096 0.077 71.808
SMC 2.1 0.766 0.066 0.064 10.959
SMC 3.0 0.134 0.091 0.084 0.507
SMC 4.0 0.072 0.079 0.090 -0.074
SMC 10.0 0.117 0.091 0.079 0.320
SMC 50.0 0.123 0.096 0.077 0.352
Metro 2.1 0.362 0.066 0.064 4.636
Metro 3.0 0.825 0.091 0.084 8.708
Metro 4.0 1.158 0.079 0.090 11.986
Metro 10.0 5.338 0.091 0.079 66.162
Metro 50.0 5.574 0.096 0.077 71.590
DEMetro_Z 2.1 1.609 0.066 0.064 24.150
DEMetro_Z 3.0 1.672 0.091 0.084 18.755
DEMetro_Z 4.0 2.040 0.079 0.090 21.786
DEMetro_Z 10.0 2.561 0.091 0.079 31.137
DEMetro_Z 50.0 4.768 0.096 0.077 61.054
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 0.283 0.781 0.208
HMC 3.0 3.685 0.00284 3.946
HMC 4.0 3.681 0.00362 105.283
HMC 10.0 15.035 1.1e-08 174.452
HMC 50.0 703.170 2.57e-49 282.170
SMC 2.1 -1.527 0.155 -0.442
SMC 3.0 -0.872 0.395 -0.286
SMC 4.0 1.335 0.203 1.075
SMC 10.0 -1.635 0.121 -0.532
SMC 50.0 -0.592 0.56 -0.266
Metro 2.1 -1.594 0.139 -0.461
Metro 3.0 1.250 0.237 5.791
Metro 4.0 1.413 0.185 41.127
Metro 10.0 14.009 2.31e-08 177.434
Metro 50.0 701.162 2.64e-49 282.152
DEMetro_Z 2.1 -1.008 0.332 -0.303
DEMetro_Z 3.0 1.940 0.0783 13.386
DEMetro_Z 4.0 2.264 0.0448 100.671
DEMetro_Z 10.0 2.853 0.0157 79.870
DEMetro_Z 50.0 7.389 1.38e-05 234.923
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.967 0.354 0.279
HMC_vs_SMC 1 3.901 0.00247 1.126
HMC_vs_SMC 2 3.631 0.00395 1.048
HMC_vs_SMC 3 15.149 1.03e-08 4.373
HMC_vs_SMC 4 619.001 2.46e-26 178.690
Metro_vs_DEMetro_Z 0 -1.914 0.082 -0.553
Metro_vs_DEMetro_Z 1 -0.844 0.417 -0.244
Metro_vs_DEMetro_Z 2 -1.023 0.328 -0.295
Metro_vs_DEMetro_Z 3 2.820 0.0167 0.814
Metro_vs_DEMetro_Z 4 1.491 0.164 0.430
HMC_vs_Metro 0 0.986 0.345 0.285
HMC_vs_Metro 1 -0.360 0.725 -0.104
HMC_vs_Metro 2 2.417 0.0342 0.698
HMC_vs_Metro 3 -0.165 0.872 -0.048
HMC_vs_Metro 4 0.236 0.818 0.068
HMC_vs_DEMetro_Z 0 0.737 0.477 0.213
HMC_vs_DEMetro_Z 1 -1.347 0.205 -0.389
HMC_vs_DEMetro_Z 2 0.077 0.94 0.022
HMC_vs_DEMetro_Z 3 3.590 0.00425 1.036
HMC_vs_DEMetro_Z 4 1.490 0.164 0.430
Metro_vs_SMC 0 -1.027 0.326 -0.297
Metro_vs_SMC 1 1.292 0.223 0.373
Metro_vs_SMC 2 1.363 0.2 0.394
Metro_vs_SMC 3 14.095 2.19e-08 4.069
Metro_vs_SMC 4 594.398 3.84e-26 171.588
DEMetro_Z_vs_SMC 0 1.824 0.0954 0.527
DEMetro_Z_vs_SMC 1 1.974 0.0741 0.570
DEMetro_Z_vs_SMC 2 2.246 0.0462 0.648
DEMetro_Z_vs_SMC 3 2.870 0.0152 0.829
DEMetro_Z_vs_SMC 4 7.380 1.39e-05 2.130
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 37.344 26.699 51.062 0.208
HMC 3.0 3.167 0.764 0.609 3.946
HMC 4.0 13.990 0.284 0.130 105.283
HMC 10.0 41.630 0.283 0.237 174.452
HMC 50.0 45.233 0.268 0.159 282.170
SMC 2.1 4.139 26.699 51.062 -0.442
SMC 3.0 0.590 0.764 0.609 -0.286
SMC 4.0 0.424 0.284 0.130 1.075
SMC 10.0 0.157 0.283 0.237 -0.532
SMC 50.0 0.226 0.268 0.159 -0.266
Metro 2.1 3.181 26.699 51.062 -0.461
Metro 3.0 4.291 0.764 0.609 5.791
Metro 4.0 5.638 0.284 0.130 41.127
Metro 10.0 42.337 0.283 0.237 177.434
Metro 50.0 45.230 0.268 0.159 282.152
DEMetro_Z 2.1 11.230 26.699 51.062 -0.303
DEMetro_Z 3.0 8.917 0.764 0.609 13.386
DEMetro_Z 4.0 13.390 0.284 0.130 100.671
DEMetro_Z 10.0 19.213 0.283 0.237 79.870
DEMetro_Z 50.0 37.704 0.268 0.159 234.923
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.926 0.0134 6.779
HMC 3.0 6.446 4.21e-05 15.988
HMC 4.0 5.227 0.000278 32.952
HMC 10.0 21.962 1.43e-10 64.631
HMC 50.0 45.810 1.77e-14 80.690
SMC 2.1 3.372 0.00587 6.513
SMC 3.0 1.234 0.231 0.565
SMC 4.0 -0.177 0.862 -0.055
SMC 10.0 0.508 0.617 0.190
SMC 50.0 0.677 0.506 0.288
Metro 2.1 4.062 0.000879 2.602
Metro 3.0 1.766 0.105 10.028
Metro 4.0 2.186 0.0512 14.255
Metro 10.0 20.228 3.74e-10 66.422
Metro 50.0 43.527 3.34e-14 78.004
DEMetro_Z 2.1 3.188 0.00853 13.297
DEMetro_Z 3.0 3.155 0.00911 19.724
DEMetro_Z 4.0 2.940 0.0134 25.831
DEMetro_Z 10.0 3.085 0.0104 30.633
DEMetro_Z 50.0 7.728 8.93e-06 64.883
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -2.540 0.0275 -0.733
Metro_vs_DEMetro_Z 1 -1.004 0.337 -0.290
Metro_vs_DEMetro_Z 2 -0.940 0.368 -0.271
Metro_vs_DEMetro_Z 3 3.087 0.0103 0.891
Metro_vs_DEMetro_Z 4 1.587 0.141 0.458
DEMetro_Z_vs_SMC 0 1.717 0.114 0.496
DEMetro_Z_vs_SMC 1 3.056 0.0109 0.882
DEMetro_Z_vs_SMC 2 2.948 0.0132 0.851
DEMetro_Z_vs_SMC 3 3.086 0.0104 0.891
DEMetro_Z_vs_SMC 4 7.714 9.22e-06 2.227
HMC_vs_DEMetro_Z 0 -1.296 0.221 -0.374
HMC_vs_DEMetro_Z 1 -0.549 0.594 -0.159
HMC_vs_DEMetro_Z 2 0.547 0.595 0.158
HMC_vs_DEMetro_Z 3 3.429 0.00564 0.990
HMC_vs_DEMetro_Z 4 1.709 0.116 0.493
HMC_vs_Metro 0 2.096 0.06 0.605
HMC_vs_Metro 1 0.814 0.433 0.235
HMC_vs_Metro 2 3.098 0.0101 0.894
HMC_vs_Metro 3 -0.391 0.703 -0.113
HMC_vs_Metro 4 0.987 0.345 0.285
HMC_vs_SMC 0 0.125 0.903 0.036
HMC_vs_SMC 1 6.262 6.16e-05 1.808
HMC_vs_SMC 2 5.265 0.000267 1.520
HMC_vs_SMC 3 22.724 1.35e-10 6.560
HMC_vs_SMC 4 43.133 1.27e-13 12.451
Metro_vs_SMC 0 -1.945 0.0778 -0.561
Metro_vs_SMC 1 1.657 0.126 0.478
Metro_vs_SMC 2 2.208 0.0494 0.638
Metro_vs_SMC 3 19.603 6.63e-10 5.659
Metro_vs_SMC 4 39.686 3.15e-13 11.456
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.843 0.182 0.098 6.779
HMC 3.0 1.248 0.130 0.070 15.988
HMC 4.0 2.441 0.108 0.071 32.952
HMC 10.0 4.730 0.110 0.071 64.631
HMC 50.0 5.104 0.106 0.062 80.690
SMC 2.1 0.817 0.182 0.098 6.513
SMC 3.0 0.170 0.130 0.070 0.565
SMC 4.0 0.104 0.108 0.071 -0.055
SMC 10.0 0.124 0.110 0.071 0.190
SMC 50.0 0.124 0.106 0.062 0.288
Metro 2.1 0.436 0.182 0.098 2.602
Metro 3.0 0.831 0.130 0.070 10.028
Metro 4.0 1.117 0.108 0.071 14.255
Metro 10.0 4.858 0.110 0.071 66.422
Metro 50.0 4.937 0.106 0.062 78.004
DEMetro_Z 2.1 1.479 0.182 0.098 13.297
DEMetro_Z 3.0 1.509 0.130 0.070 19.724
DEMetro_Z 4.0 1.937 0.108 0.071 25.831
DEMetro_Z 10.0 2.300 0.110 0.071 30.633
DEMetro_Z 50.0 4.125 0.106 0.062 64.883
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 4.067 0.00179 11.536
HMC 3.0 6.430 4.39e-05 17.397
HMC 4.0 5.384 0.000218 32.294
HMC 10.0 25.967 2.13e-11 70.606
HMC 50.0 108.942 2.69e-23 78.053
SMC 2.1 2.947 0.0132 12.681
SMC 3.0 1.331 0.198 0.655
SMC 4.0 -0.167 0.87 -0.052
SMC 10.0 0.979 0.338 0.387
SMC 50.0 0.863 0.397 0.347
Metro 2.1 3.921 0.00191 4.620
Metro 3.0 1.789 0.101 10.309
Metro 4.0 2.323 0.0403 13.230
Metro 10.0 21.055 2.43e-10 69.724
Metro 50.0 142.952 1.07e-29 77.329
DEMetro_Z 2.1 2.844 0.0159 28.680
DEMetro_Z 3.0 2.958 0.013 22.757
DEMetro_Z 4.0 2.927 0.0137 23.945
DEMetro_Z 10.0 3.129 0.00958 33.530
DEMetro_Z 50.0 7.751 8.69e-06 65.037
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 1.687 0.12 0.487
DEMetro_Z_vs_SMC 1 2.856 0.0156 0.824
DEMetro_Z_vs_SMC 2 2.931 0.0137 0.846
DEMetro_Z_vs_SMC 3 3.119 0.00977 0.900
DEMetro_Z_vs_SMC 4 7.726 9.09e-06 2.230
HMC_vs_Metro 0 3.023 0.0116 0.873
HMC_vs_Metro 1 0.935 0.37 0.270
HMC_vs_Metro 2 3.582 0.0043 1.034
HMC_vs_Metro 3 0.203 0.843 0.059
HMC_vs_Metro 4 0.995 0.341 0.287
Metro_vs_DEMetro_Z 0 -2.325 0.0402 -0.671
Metro_vs_DEMetro_Z 1 -1.135 0.28 -0.328
Metro_vs_DEMetro_Z 2 -0.953 0.361 -0.275
Metro_vs_DEMetro_Z 3 2.963 0.0129 0.855
Metro_vs_DEMetro_Z 4 1.500 0.162 0.433
HMC_vs_SMC 0 -0.271 0.792 -0.078
HMC_vs_SMC 1 6.235 6.39e-05 1.800
HMC_vs_SMC 2 5.425 0.000209 1.566
HMC_vs_SMC 3 26.721 2.34e-11 7.714
HMC_vs_SMC 4 97.318 1.68e-17 28.093
Metro_vs_SMC 0 -1.819 0.0962 -0.525
Metro_vs_SMC 1 1.663 0.124 0.480
Metro_vs_SMC 2 2.350 0.0385 0.678
Metro_vs_SMC 3 19.895 5.65e-10 5.743
Metro_vs_SMC 4 141.032 2.85e-19 40.712
HMC_vs_DEMetro_Z 0 -1.530 0.154 -0.442
HMC_vs_DEMetro_Z 1 -0.639 0.536 -0.184
HMC_vs_DEMetro_Z 2 0.686 0.507 0.198
HMC_vs_DEMetro_Z 3 3.633 0.00394 1.049
HMC_vs_DEMetro_Z 4 1.521 0.156 0.439
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.075 0.009 0.006 11.536
HMC 3.0 0.146 0.010 0.008 17.397
HMC 4.0 0.300 0.009 0.009 32.294
HMC 10.0 0.594 0.010 0.008 70.606
HMC 50.0 0.615 0.010 0.008 78.053
SMC 2.1 0.082 0.009 0.006 12.681
SMC 3.0 0.015 0.010 0.008 0.655
SMC 4.0 0.009 0.009 0.009 -0.052
SMC 10.0 0.014 0.010 0.008 0.387
SMC 50.0 0.013 0.010 0.008 0.347
Metro 2.1 0.035 0.009 0.006 4.620
Metro 3.0 0.090 0.010 0.008 10.309
Metro 4.0 0.128 0.009 0.009 13.230
Metro 10.0 0.587 0.010 0.008 69.724
Metro 50.0 0.609 0.010 0.008 77.329
DEMetro_Z 2.1 0.174 0.009 0.006 28.680
DEMetro_Z 3.0 0.188 0.010 0.008 22.757
DEMetro_Z 4.0 0.225 0.009 0.009 23.945
DEMetro_Z 10.0 0.288 0.010 0.008 33.530
DEMetro_Z 50.0 0.514 0.010 0.008 65.037
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Forest & Ridge Plots
Pooled
2.1 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
50 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2.1 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
50 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2.1
3
4
10
50
Chain
2.1
3
4
10
50